判定梅森质数的卢卡斯序列

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

Treenewbee

穷举一定范围，用返回结果搜索OEIS即可

1. Select[Range[10^7], DivisorSigma[1, #] == 4 # &]
   

复制代码

{30240, 32760, 2178540}

Treenewbee

蔡家雄 发表于 2023-11-27 13:52
猜想：真分数 10/m=1/x+1/y+1/z 有的无解，

猜想：真分数 11/m=1/x+1/y+1/z 都有解，

12-10000穷举了一下，m=37时,真分数 11/m=1/x+1/y+1/z 无解。

Treenewbee

蔡家雄 发表于 2023-11-27 13:52
猜想：真分数 10/m=1/x+1/y+1/z 有的无解，

猜想：真分数 11/m=1/x+1/y+1/z 都有解，

11-10000穷举了一下，m={11, 43, 61, 67, 181}时,真分数 10/m=1/x+1/y+1/z 无解。

Treenewbee

蔡家雄 发表于 2023-11-25 10:27
zengyong 的

4/9241=1/2314+1/164498+1/10691837 ——计算错误！

\[\frac{4}{9241}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\]搜到了49组解(x<y<z)：

{{2312,3052180,958976642920},{2312,3052248,119874751014},{2312,3053574,6639547608},{2312,3063400,832614100},{2312,3141940,106825960},{2312,3770328,16023894},{2314,1425580,1172466845420},{2314,1425602,85630922533},{2314,1426581,2028159234},{2314,1439308,149445452},{2314,1441596,128302044},{2314,1644898,10691837},{2318,702316,42841276},{2320,549724,101599989680},{2320,549840,2540535720},{2320,554460,64317360},{2320,554480,64049371},{2320,739280,2143912},{2321,498804,50703925404},{2321,499014,1158211494},{2322,457434,234841533},{2323,425086,42933686},{2325,462050,1718826},{2330,272610,1259594505},{2332,247775,832614100},{2336,209583,61976208096},{2340,181714,151129716660},{2340,181740,1259594505},{2340,181935,149445452},{2340,184820,10811970},{2350,136582,15776928275},{2356,118978,2198951396},{2364,101651,240302964},{2364,101652,234841533},{2366,98046,41224960413},{2370,91640,2540535720},{2370,92410,10950585},{2386,72773,1344990586},{2390,69310,64049371},{2418,51844,44555407572},{2466,36579,2028159234},{2488,32344,149445452},{2496,31044,4590041664},{2650,18020,832614100},{2691,16328,31233618936},{2703,15900,832614100},{2782,13624,13471234088},{3400,7208,832614100},{3480,6873,2540535720}}

Treenewbee

蔡家雄 发表于 2023-11-23 18:16
请教王老师的

5/541=1/ 110+1/6615+1/15746346

\[\frac{5}{541}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] 搜到了16组解(x<y<z)：

{{110,6615,15746346},{110,6666,819615},{110,8115,35706},{111,4290,28624310},{111,4292,6965916},{111,4328,480408},{112,3192,3453744},{112,3246,181776},{114,2127,14575622},{114,2128,3453744},{114,2164,123348},{115,1830,22770690},{116,1623,188268},{121,1023,6087873},{134,562,10185407},{168,304,3453744}}

白新岭

做的很好！继续努力！

Treenewbee

\[\frac{5}{2341}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] 搜到了26组解(x<y<z)：

{{469,274484,43051991948},{469,274499,4498215113},{469,275303,92069189},{469,278579,18664793},{469,282338,9864974},{469,313694,2195858},{470,122255,5380540354},{470,123234,15345255},{470,128755,2420594},{471,78758,86839437138},{473,46139,1188125389},{473,46354,9864974},{475,32774,15567650},{475,32775,15345255},{482,16387,7898534},{483,15295,15345255},{490,10535,9864974},{494,8970,15345255},{506,6270,15345255},{528,4134,283879024},{570,2622,15345255},{576,2502,20825536},{602,2107,9864974},{735,1290,9864974},{786,1158,59187503},{855,1035,15345255}}

王守恩

Treenewbee 发表于 2023-11-27 15:38
\[\frac{4}{9241}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\]搜到了49组解(x

题目:  4/m=1/x+1/y+1/z,   其中m,x,y,z均为正整数, 我们约定x≤y≤z。
猜想：x={m/4+0,m/4+1,m/4+2,m/4+3,m/4+4,m/4+5}, x只要取遍这6个数, 肯定有解。
这个程怎么编，我还是不会,最好直接来一个反例,  谢谢！