[原创数论小题]神气的3位数

ysr

[这个贴子最后由ysr在 2014/04/16 01:54pm 第 1 次编辑]

3位数376乘以某些3位数,得数的末尾3位数仍然是该数,如376*288=288(MOD1000),376*112=112(MOD1000)等,问:有多少3位数乘以376得数的末尾3位数仍然是该数?
(注意:000,012等不是3位数)

ysr

手工计算麻烦，用电脑则一切简单，如下为结果，找到相同的数1下个数就可以：
100,37600,600
101,37976,976
102,38352,352
103,38728,728
104,39104,104
105,39480,480
106,39856,856
107,40232,232
108,40608,608
109,40984,984
110,41360,360
111,41736,736
112,42112,112
113,42488,488
114,42864,864
115,43240,240
116,43616,616
117,43992,992
118,44368,368
119,44744,744
120,45120,120
121,45496,496
122,45872,872
123,46248,248
124,46624,624
125,47000,0
126,47376,376
127,47752,752
128,48128,128
129,48504,504
130,48880,880
131,49256,256
132,49632,632
133,50008,8
134,50384,384
135,50760,760
136,51136,136
137,51512,512
138,51888,888
139,52264,264
140,52640,640
141,53016,16
142,53392,392
143,53768,768
144,54144,144
145,54520,520
146,54896,896
147,55272,272
148,55648,648
149,56024,24
150,56400,400
151,56776,776
152,57152,152
153,57528,528
154,57904,904
155,58280,280
156,58656,656
157,59032,32
158,59408,408
159,59784,784
160,60160,160
161,60536,536
162,60912,912
163,61288,288
164,61664,664
165,62040,40
166,62416,416
167,62792,792
168,63168,168
169,63544,544
170,63920,920
171,64296,296
172,64672,672
173,65048,48
174,65424,424
175,65800,800
176,66176,176
177,66552,552
178,66928,928
179,67304,304
180,67680,680
181,68056,56
182,68432,432
183,68808,808
184,69184,184
185,69560,560
186,69936,936
187,70312,312
188,70688,688
189,71064,64
190,71440,440
191,71816,816
192,72192,192
193,72568,568
194,72944,944
195,73320,320
196,73696,696
197,74072,72
198,74448,448
199,74824,824
200,75200,200
201,75576,576
202,75952,952
203,76328,328
204,76704,704
205,77080,80
206,77456,456
207,77832,832
208,78208,208
209,78584,584
210,78960,960
211,79336,336
212,79712,712
213,80088,88
214,80464,464
215,80840,840
216,81216,216
217,81592,592
218,81968,968
219,82344,344
220,82720,720
221,83096,96
222,83472,472
223,83848,848
224,84224,224
225,84600,600
226,84976,976
227,85352,352
228,85728,728
229,86104,104
230,86480,480
231,86856,856
232,87232,232
233,87608,608
234,87984,984
235,88360,360
236,88736,736
237,89112,112
238,89488,488
239,89864,864
240,90240,240
241,90616,616
242,90992,992
243,91368,368
244,91744,744
245,92120,120
246,92496,496
247,92872,872
248,93248,248
249,93624,624
250,94000,0
251,94376,376
252,94752,752
253,95128,128
254,95504,504
255,95880,880
256,96256,256
257,96632,632
258,97008,8
259,97384,384
260,97760,760
261,98136,136
262,98512,512
263,98888,888
264,99264,264
265,99640,640
266,100016,16
267,100392,392
268,100768,768
269,101144,144
270,101520,520
271,101896,896
272,102272,272
273,102648,648
274,103024,24
275,103400,400
276,103776,776
277,104152,152
278,104528,528
279,104904,904
280,105280,280
281,105656,656
282,106032,32
283,106408,408
284,106784,784
285,107160,160
286,107536,536
287,107912,912
288,108288,288
289,108664,664
290,109040,40
291,109416,416
292,109792,792
293,110168,168
294,110544,544
295,110920,920
296,111296,296
297,111672,672
298,112048,48
299,112424,424
300,112800,800
301,113176,176
302,113552,552
303,113928,928
304,114304,304
305,114680,680
306,115056,56
307,115432,432
308,115808,808
309,116184,184
310,116560,560
311,116936,936
312,117312,312
313,117688,688
314,118064,64
315,118440,440
316,118816,816
317,119192,192
318,119568,568
319,119944,944
320,120320,320
321,120696,696
322,121072,72
323,121448,448
324,121824,824
325,122200,200
326,122576,576
327,122952,952
328,123328,328
329,123704,704
330,124080,80
331,124456,456
332,124832,832
333,125208,208
334,125584,584
335,125960,960
336,126336,336
337,126712,712
338,127088,88
339,127464,464
340,127840,840
341,128216,216
342,128592,592
343,128968,968
344,129344,344
345,129720,720
346,130096,96
347,130472,472
348,130848,848
349,131224,224
350,131600,600
351,131976,976
352,132352,352
353,132728,728
354,133104,104
355,133480,480
356,133856,856
357,134232,232
358,134608,608
359,134984,984
360,135360,360
361,135736,736
362,136112,112
363,136488,488
364,136864,864
365,137240,240
366,137616,616
367,137992,992
368,138368,368
369,138744,744
370,139120,120
371,139496,496
372,139872,872
373,140248,248
374,140624,624
375,141000,0
376,141376,376
377,141752,752
378,142128,128
379,142504,504
380,142880,880
381,143256,256
382,143632,632
383,144008,8
384,144384,384
385,144760,760
386,145136,136
387,145512,512
388,145888,888
389,146264,264
390,146640,640
391,147016,16
392,147392,392
393,147768,768
394,148144,144
395,148520,520
396,148896,896
397,149272,272
398,149648,648
399,150024,24
400,150400,400
401,150776,776
402,151152,152
403,151528,528
404,151904,904
405,152280,280
406,152656,656
407,153032,32
408,153408,408
409,153784,784
410,154160,160
411,154536,536
412,154912,912
413,155288,288
414,155664,664
415,156040,40
416,156416,416
417,156792,792
418,157168,168
419,157544,544
420,157920,920
421,158296,296
422,158672,672
423,159048,48
424,159424,424
425,159800,800
426,160176,176
427,160552,552
428,160928,928
429,161304,304
430,161680,680
431,162056,56
432,162432,432
433,162808,808
434,163184,184
435,163560,560
436,163936,936
437,164312,312
438,164688,688
439,165064,64
440,165440,440
441,165816,816
442,166192,192
443,166568,568
444,166944,944
445,167320,320
446,167696,696
447,168072,72
448,168448,448
449,168824,824
450,169200,200
451,169576,576
452,169952,952
453,170328,328
454,170704,704
455,171080,80
456,171456,456
457,171832,832
458,172208,208
459,172584,584
460,172960,960
461,173336,336
462,173712,712
463,174088,88
464,174464,464
465,174840,840
466,175216,216
467,175592,592
468,175968,968
469,176344,344
470,176720,720
471,177096,96
472,177472,472
473,177848,848
474,178224,224
475,178600,600
476,178976,976
477,179352,352
478,179728,728
479,180104,104
480,180480,480
481,180856,856
482,181232,232
483,181608,608
484,181984,984
485,182360,360
486,182736,736
487,183112,112
488,183488,488
489,183864,864
490,184240,240
491,184616,616
492,184992,992
493,185368,368
494,185744,744
495,186120,120
496,186496,496
497,186872,872
498,187248,248
499,187624,624
500,188000,0
501,188376,376
502,188752,752
503,189128,128
504,189504,504
505,189880,880
506,190256,256
507,190632,632
508,191008,8
509,191384,384
510,191760,760
511,192136,136
512,192512,512
513,192888,888
514,193264,264
515,193640,640
516,194016,16
517,194392,392
518,194768,768
519,195144,144
520,195520,520
521,195896,896
522,196272,272
523,196648,648
524,197024,24
525,197400,400
526,197776,776
527,198152,152
528,198528,528
529,198904,904
530,199280,280
531,199656,656
532,200032,32
533,200408,408
534,200784,784
535,201160,160
536,201536,536
537,201912,912
538,202288,288
539,202664,664
540,203040,40
541,203416,416
542,203792,792
543,204168,168
544,204544,544
545,204920,920
546,205296,296
547,205672,672
548,206048,48
549,206424,424
550,206800,800
551,207176,176
552,207552,552
553,207928,928
554,208304,304
555,208680,680
556,209056,56
557,209432,432
558,209808,808
559,210184,184
560,210560,560
561,210936,936
562,211312,312
563,211688,688
564,212064,64
565,212440,440
566,212816,816
567,213192,192
568,213568,568
569,213944,944
570,214320,320
571,214696,696
572,215072,72
573,215448,448
574,215824,824
575,216200,200
576,216576,576
577,216952,952
578,217328,328
579,217704,704
580,218080,80
581,218456,456
582,218832,832
583,219208,208
584,219584,584
585,219960,960
586,220336,336
587,220712,712
588,221088,88
589,221464,464
590,221840,840
591,222216,216
592,222592,592
593,222968,968
594,223344,344
595,223720,720
596,224096,96
597,224472,472
598,224848,848
599,225224,224
600,225600,600
601,225976,976
602,226352,352
603,226728,728
604,227104,104
605,227480,480
606,227856,856
607,228232,232
608,228608,608
609,228984,984
610,229360,360
611,229736,736
612,230112,112
613,230488,488
614,230864,864
615,231240,240
616,231616,616
617,231992,992
618,232368,368
619,232744,744
620,233120,120
621,233496,496
622,233872,872
623,234248,248
624,234624,624
625,235000,0
626,235376,376
627,235752,752
628,236128,128
629,236504,504
630,236880,880
631,237256,256
632,237632,632
633,238008,8
634,238384,384
635,238760,760
636,239136,136
637,239512,512
638,239888,888
639,240264,264
640,240640,640
641,241016,16
642,241392,392
643,241768,768
644,242144,144
645,242520,520
646,242896,896
647,243272,272
648,243648,648
649,244024,24
650,244400,400
651,244776,776
652,245152,152
653,245528,528
654,245904,904
655,246280,280
656,246656,656
657,247032,32
658,247408,408
659,247784,784
660,248160,160
661,248536,536
662,248912,912
663,249288,288
664,249664,664
665,250040,40
666,250416,416
667,250792,792
668,251168,168
669,251544,544
670,251920,920
671,252296,296
672,252672,672
673,253048,48
674,253424,424
675,253800,800
676,254176,176
677,254552,552
678,254928,928
679,255304,304
680,255680,680
681,256056,56
682,256432,432
683,256808,808
684,257184,184
685,257560,560
686,257936,936
687,258312,312
688,258688,688
689,259064,64
690,259440,440
691,259816,816
692,260192,192
693,260568,568
694,260944,944
695,261320,320
696,261696,696
697,262072,72
698,262448,448
699,262824,824
700,263200,200
701,263576,576
702,263952,952
703,264328,328
704,264704,704
705,265080,80
706,265456,456
707,265832,832
708,266208,208
709,266584,584
710,266960,960
711,267336,336
712,267712,712
713,268088,88
714,268464,464
715,268840,840
716,269216,216
717,269592,592
718,269968,968
719,270344,344
720,270720,720
721,271096,96
722,271472,472
723,271848,848
724,272224,224
725,272600,600
726,272976,976
727,273352,352
728,273728,728
729,274104,104
730,274480,480
731,274856,856
732,275232,232
733,275608,608
734,275984,984
735,276360,360
736,276736,736
737,277112,112
738,277488,488
739,277864,864
740,278240,240
741,278616,616
742,278992,992
743,279368,368
744,279744,744
745,280120,120
746,280496,496
747,280872,872
748,281248,248
749,281624,624
750,282000,0
751,282376,376
752,282752,752
753,283128,128
754,283504,504
755,283880,880
756,284256,256
757,284632,632
758,285008,8
759,285384,384
760,285760,760
761,286136,136
762,286512,512
763,286888,888
764,287264,264
765,287640,640
766,288016,16
767,288392,392
768,288768,768
769,289144,144
770,289520,520
771,289896,896
772,290272,272
773,290648,648
774,291024,24
775,291400,400
776,291776,776
777,292152,152
778,292528,528
779,292904,904
780,293280,280
781,293656,656
782,294032,32
783,294408,408
784,294784,784
785,295160,160
786,295536,536
787,295912,912
788,296288,288
789,296664,664
790,297040,40
791,297416,416
792,297792,792
793,298168,168
794,298544,544
795,298920,920
796,299296,296
797,299672,672
798,300048,48
799,300424,424
800,300800,800
801,301176,176
802,301552,552
803,301928,928
804,302304,304
805,302680,680
806,303056,56
807,303432,432
808,303808,808
809,304184,184
810,304560,560
811,304936,936
812,305312,312
813,305688,688
814,306064,64
815,306440,440
816,306816,816
817,307192,192
818,307568,568
819,307944,944
820,308320,320
821,308696,696
822,309072,72
823,309448,448
824,309824,824
825,310200,200
826,310576,576
827,310952,952
828,311328,328
829,311704,704
830,312080,80
831,312456,456
832,312832,832
833,313208,208
834,313584,584
835,313960,960
836,314336,336
837,314712,712
838,315088,88
839,315464,464
840,315840,840
841,316216,216
842,316592,592
843,316968,968
844,317344,344
845,317720,720
846,318096,96
847,318472,472
848,318848,848
849,319224,224
850,319600,600
851,319976,976
852,320352,352
853,320728,728
854,321104,104
855,321480,480
856,321856,856
857,322232,232
858,322608,608
859,322984,984
860,323360,360
861,323736,736
862,324112,112
863,324488,488
864,324864,864
865,325240,240
866,325616,616
867,325992,992
868,326368,368
869,326744,744
870,327120,120
871,327496,496
872,327872,872
873,328248,248
874,328624,624
875,329000,0
876,329376,376
877,329752,752
878,330128,128
879,330504,504
880,330880,880
881,331256,256
882,331632,632
883,332008,8
884,332384,384
885,332760,760
886,333136,136
887,333512,512
888,333888,888
889,334264,264
890,334640,640
891,335016,16
892,335392,392
893,335768,768
894,336144,144
895,336520,520
896,336896,896
897,337272,272
898,337648,648
899,338024,24
900,338400,400
901,338776,776
902,339152,152
903,339528,528
904,339904,904
905,340280,280
906,340656,656
907,341032,32
908,341408,408
909,341784,784
910,342160,160
911,342536,536
912,342912,912
913,343288,288
914,343664,664
915,344040,40
916,344416,416
917,344792,792
918,345168,168
919,345544,544
920,345920,920
921,346296,296
922,346672,672
923,347048,48
924,347424,424
925,347800,800
926,348176,176
927,348552,552
928,348928,928
929,349304,304
930,349680,680
931,350056,56
932,350432,432
933,350808,808
934,351184,184
935,351560,560
936,351936,936
937,352312,312
938,352688,688
939,353064,64
940,353440,440
941,353816,816
942,354192,192
943,354568,568
944,354944,944
945,355320,320
946,355696,696
947,356072,72
948,356448,448
949,356824,824
950,357200,200
951,357576,576
952,357952,952
953,358328,328
954,358704,704
955,359080,80
956,359456,456
957,359832,832
958,360208,208
959,360584,584
960,360960,960
961,361336,336
962,361712,712
963,362088,88
964,362464,464
965,362840,840
966,363216,216
967,363592,592
968,363968,968
969,364344,344
970,364720,720
971,365096,96
972,365472,472
973,365848,848
974,366224,224
975,366600,600
976,366976,976
977,367352,352
978,367728,728
979,368104,104
980,368480,480
981,368856,856
982,369232,232
983,369608,608
984,369984,984
985,370360,360
986,370736,736
987,371112,112
988,371488,488
989,371864,864
990,372240,240
991,372616,616
992,372992,992
993,373368,368
994,373744,744
995,374120,120
996,374496,496
997,374872,872
998,375248,248
999,375624,624

ysr

300前找到19个，且余数行有多个相同的，若把相同的数字改变，作成一一对应的，可以做为一种密码的加密方法。

ysr

[这个贴子最后由ysr在 2014/04/18 01:06pm 第 1 次编辑]

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857,322232,232,-625
858,322608,608,-250
859,322984,984,125
860,323360,360,-500
861,323736,736,-125
862,324112,112,-750
863,324488,488,-375
864,324864,864,0
865,325240,240,-625
866,325616,616,-250
867,325992,992,125
868,326368,368,-500
869,326744,744,-125
870,327120,120,-750
871,327496,496,-375
872,327872,872,0
873,328248,248,-625
874,328624,624,-250
875,329000,0,-875
876,329376,376,-500
877,329752,752,-125
878,330128,128,-750
879,330504,504,-375
880,330880,880,0
881,331256,256,-625
882,331632,632,-250
883,332008,8,-875
884,332384,384,-500
885,332760,760,-125
886,333136,136,-750
887,333512,512,-375
888,333888,888,0
889,334264,264,-625
890,334640,640,-250
891,335016,16,-875
892,335392,392,-500
893,335768,768,-125
894,336144,144,-750
895,336520,520,-375
896,336896,896,0
897,337272,272,-625
898,337648,648,-250
899,338024,24,-875
900,338400,400,-500
901,338776,776,-125
902,339152,152,-750
903,339528,528,-375
904,339904,904,0
905,340280,280,-625
906,340656,656,-250
907,341032,32,-875
908,341408,408,-500
909,341784,784,-125
910,342160,160,-750
911,342536,536,-375
912,342912,912,0
913,343288,288,-625
914,343664,664,-250
915,344040,40,-875
916,344416,416,-500
917,344792,792,-125
918,345168,168,-750
919,345544,544,-375
920,345920,920,0
921,346296,296,-625
922,346672,672,-250
923,347048,48,-875
924,347424,424,-500
925,347800,800,-125
926,348176,176,-750
927,348552,552,-375
928,348928,928,0
929,349304,304,-625
930,349680,680,-250
931,350056,56,-875
932,350432,432,-500
933,350808,808,-125
934,351184,184,-750
935,351560,560,-375
936,351936,936,0
937,352312,312,-625
938,352688,688,-250
939,353064,64,-875
940,353440,440,-500
941,353816,816,-125
942,354192,192,-750
943,354568,568,-375
944,354944,944,0
945,355320,320,-625
946,355696,696,-250
947,356072,72,-875
948,356448,448,-500
949,356824,824,-125
950,357200,200,-750
951,357576,576,-375
952,357952,952,0
953,358328,328,-625
954,358704,704,-250
955,359080,80,-875
956,359456,456,-500
957,359832,832,-125
958,360208,208,-750
959,360584,584,-375
960,360960,960,0
961,361336,336,-625
962,361712,712,-250
963,362088,88,-875
964,362464,464,-500
965,362840,840,-125
966,363216,216,-750
967,363592,592,-375
968,363968,968,0
969,364344,344,-625
970,364720,720,-250
971,365096,96,-875
972,365472,472,-500
973,365848,848,-125
974,366224,224,-750
975,366600,600,-375
976,366976,976,0
977,367352,352,-625
978,367728,728,-250
979,368104,104,-875
980,368480,480,-500
981,368856,856,-125
982,369232,232,-750
983,369608,608,-375
984,369984,984,0
985,370360,360,-625
986,370736,736,-250
987,371112,112,-875
988,371488,488,-500
989,371864,864,-125
990,372240,240,-750
991,372616,616,-375
992,372992,992,0
993,373368,368,-625
994,373744,744,-250
995,374120,120,-875
996,374496,496,-500
997,374872,872,-125
998,375248,248,-750
999,375624,624,-375
是112个把，就是最后1纵行为0的个数

ysr

[这个贴子最后由ysr在 2014/04/18 01:29pm 第 2 次编辑]

如下为1-----999乘以376，MOD10000的余数，好象没有重复的，要是程序检验没有重复的就可以用来做密码，原文是3位的密码是4位的，密文加长了，不知道对应规则是很难破解的，手工很难做，程序就简单了，高手很容易做的，理论上信息长度不限，对我来说，字符不超过20000，否则内存会溢出。对应规则是不能发布要保密，只要做好加解密程序送给对方，这样你们之间就建立了绝对秘密的通道。回头验证1下，感兴趣的不妨实验1下：
376
752
1128
1504
1880
2256
2632
3008
3384
3760
4136
4512
4888
5264
5640
6016
6392
6768
7144
7520
7896
8272
8648
9024
9400
9776
152
528
904
1280
1656
2032
2408
2784
3160
3536
3912
4288
4664
5040
5416
5792
6168
6544
6920
7296
7672
8048
8424
8800
9176
9552
9928
304
680
1056
1432
1808
2184
2560
2936
3312
3688
4064
4440
4816
5192
5568
5944
6320
6696
7072
7448
7824
8200
8576
8952
9328
9704
80
456
832
1208
1584
1960
2336
2712
3088
3464
3840
4216
4592
4968
5344
5720
6096
6472
6848
7224
7600
7976
8352
8728
9104
9480
9856
232
608
984
1360
1736
2112
2488
2864
3240
3616
3992
4368
4744
5120
5496
5872
6248
6624
7000
7376
7752
8128
8504
8880
9256
9632
8
384
760
1136
1512
1888
2264
2640
3016
3392
3768
4144
4520
4896
5272
5648
6024
6400
6776
7152
7528
7904
8280
8656
9032
9408
9784
160
536
912
1288
1664
2040
2416
2792
3168
3544
3920
4296
4672
5048
5424
5800
6176
6552
6928
7304
7680
8056
8432
8808
9184
9560
9936
312
688
1064
1440
1816
2192
2568
2944
3320
3696
4072
4448
4824
5200
5576
5952
6328
6704
7080
7456
7832
8208
8584
8960
9336
9712
88
464
840
1216
1592
1968
2344
2720
3096
3472
3848
4224
4600
4976
5352
5728
6104
6480
6856
7232
7608
7984
8360
8736
9112
9488
9864
240
616
992
1368
1744
2120
2496
2872
3248
3624
4000
4376
4752
5128
5504
5880
6256
6632
7008
7384
7760
8136
8512
8888
9264
9640
16
392
768
1144
1520
1896
2272
2648
3024
3400
3776
4152
4528
4904
5280
5656
6032
6408
6784
7160
7536
7912
8288
8664
9040
9416
9792
168
544
920
1296
1672
2048
2424
2800
3176
3552
3928
4304
4680
5056
5432
5808
6184
6560
6936
7312
7688
8064
8440
8816
9192
9568
9944
320
696
1072
1448
1824
2200
2576
2952
3328
3704
4080
4456
4832
5208
5584
5960
6336
6712
7088
7464
7840
8216
8592
8968
9344
9720
96
472
848
1224
1600
1976
2352
2728
3104
3480
3856
4232
4608
4984
5360
5736
6112
6488
6864
7240
7616
7992
8368
8744
9120
9496
9872
248
624
1000
1376
1752
2128
2504
2880
3256
3632
4008
4384
4760
5136
5512
5888
6264
6640
7016
7392
7768
8144
8520
8896
9272
9648
24
400
776
1152
1528
1904
2280
2656
3032
3408
3784
4160
4536
4912
5288
5664
6040
6416
6792
7168
7544
7920
8296
8672
9048
9424
9800
176
552
928
1304
1680
2056
2432
2808
3184
3560
3936
4312
4688
5064
5440
5816
6192
6568
6944
7320
7696
8072
8448
8824
9200
9576
9952
328
704
1080
1456
1832
2208
2584
2960
3336
3712
4088
4464
4840
5216
5592
5968
6344
6720
7096
7472
7848
8224
8600
8976
9352
9728
104
480
856
1232
1608
1984
2360
2736
3112
3488
3864
4240
4616
4992
5368
5744
6120
6496
6872
7248
7624
8000
8376
8752
9128
9504
9880
256
632
1008
1384
1760
2136
2512
2888
3264
3640
4016
4392
4768
5144
5520
5896
6272
6648
7024
7400
7776
8152
8528
8904
9280
9656
32
408
784
1160
1536
1912
2288
2664
3040
3416
3792
4168
4544
4920
5296
5672
6048
6424
6800
7176
7552
7928
8304
8680
9056
9432
9808
184
560
936
1312
1688
2064
2440
2816
3192
3568
3944
4320
4696
5072
5448
5824
6200
6576
6952
7328
7704
8080
8456
8832
9208
9584
9960
336
712
1088
1464
1840
2216
2592
2968
3344
3720
4096
4472
4848
5224
5600
5976
6352
6728
7104
7480
7856
8232
8608
8984
9360
9736
112
488
864
1240
1616
1992
2368
2744
3120
3496
3872
4248
4624
5000
5376
5752
6128
6504
6880
7256
7632
8008
8384
8760
9136
9512
9888
264
640
1016
1392
1768
2144
2520
2896
3272
3648
4024
4400
4776
5152
5528
5904
6280
6656
7032
7408
7784
8160
8536
8912
9288
9664
40
416
792
1168
1544
1920
2296
2672
3048
3424
3800
4176
4552
4928
5304
5680
6056
6432
6808
7184
7560
7936
8312
8688
9064
9440
9816
192
568
944
1320
1696
2072
2448
2824
3200
3576
3952
4328
4704
5080
5456
5832
6208
6584
6960
7336
7712
8088
8464
8840
9216
9592
9968
344
720
1096
1472
1848
2224
2600
2976
3352
3728
4104
4480
4856
5232
5608
5984
6360
6736
7112
7488
7864
8240
8616
8992
9368
9744
120
496
872
1248
1624
2000
2376
2752
3128
3504
3880
4256
4632
5008
5384
5760
6136
6512
6888
7264
7640
8016
8392
8768
9144
9520
9896
272
648
1024
1400
1776
2152
2528
2904
3280
3656
4032
4408
4784
5160
5536
5912
6288
6664
7040
7416
7792
8168
8544
8920
9296
9672
48
424
800
1176
1552
1928
2304
2680
3056
3432
3808
4184
4560
4936
5312
5688
6064
6440
6816
7192
7568
7944
8320
8696
9072
9448
9824
200
576
952
1328
1704
2080
2456
2832
3208
3584
3960
4336
4712
5088
5464
5840
6216
6592
6968
7344
7720
8096
8472
8848
9224
9600
9976
352
728
1104
1480
1856
2232
2608
2984
3360
3736
4112
4488
4864
5240
5616
5992
6368
6744
7120
7496
7872
8248
8624
9000
9376
9752
128
504
880
1256
1632
2008
2384
2760
3136
3512
3888
4264
4640
5016
5392
5768
6144
6520
6896
7272
7648
8024
8400
8776
9152
9528
9904
280
656
1032
1408
1784
2160
2536
2912
3288
3664
4040
4416
4792
5168
5544
5920
6296
6672
7048
7424
7800
8176
8552
8928
9304
9680
56
432
808
1184
1560
1936
2312
2688
3064
3440
3816
4192
4568
4944
5320
5696
6072
6448
6824
7200
7576
7952
8328
8704
9080
9456
9832
208
584
960
1336
1712
2088
2464
2840
3216
3592
3968
4344
4720
5096
5472
5848
6224
6600
6976
7352
7728
8104
8480
8856
9232
9608
9984
360
736
1112
1488
1864
2240
2616
2992
3368
3744
4120
4496
4872
5248
5624

熊一兵

很好的想法，还可以扩大这种想法

ysr

5楼的数组是不重复的，不够4位的前面补0，可以用来做密码。

ysr

已经做了 密码程序，如下为密文，感兴趣的可以破解试试：
19292509669700161184986556695049513

ysr

851290519441892025660927576225964600037111300037100000048230003711966375653000001872001113742001187200000187200111374200118720000018720011139460593492000004823000371192925096600000187200111374200118720000018720011137420011872000001872001113931215008500000482300037117437263100000018720011137420011872000001872001113742001187200000187200111390895801050000048230003711929272314000001872001113742001187200000187200111374200118720000018720011139386357134000004823000371185503521400000187200111374200118720000018720011137420011872000001872001113946058273300000482300037117437213170000018720011137420011872000001872001113742001187200000187200111392379348740000048230003711743728567000001872001113742001187200000187200111374200118720000018720011139200817236

luyuanhong

题  问:有多少 3 位数乘以 376 得数的末尾 3 位数仍然是该数?

解  设要求的 3 位数是 N 。

    因为 376×N 与 N 的末尾 3 位数相同，即有

             376×N≡N(mod 1000) 。

    所以有

          375×N=376×N-N≡0(mod 1000) 。

    也就是说，375×N 是 1000 的倍数。

    容易看出，只有当 N=8k 是 8 的倍数时，才可能有

            375×N=375×8k=3000k  ,

是 1000 的倍数。

    是 8 的倍数的 3 位数，从 104,112,120，…，一直到 984，992 ，

共有 (992-104)/8+1=112 个。