蔡家雄完全数为世纪之作

Treenewbee

楼主所谓的完美立方数，太多了,如：

38 = [6, [3, 4, 5]] + [20, [7, 14, 17]] + [36, [4, 24, 32]]
54 = [6, [3, 4, 5]] + [36, [4, 24, 32]] + [48, [24, 32, 40]]
57 = [9, [1, 6, 8]] + [30, [15, 20, 25]] + [54, [6, 36, 48]]
81 = [9, [1, 6, 8]] + [54, [6, 36, 48]] + [72, [8, 48, 64]]
138 = [9, [1, 6, 8]] + [108, [12, 72, 96]] + [111, [16, 47, 108]]
54 = [12, [6, 8, 10]] + [19, [3, 10, 18]] + [53, [29, 34, 44]]
76 = [12, [6, 8, 10]] + [40, [14, 28, 34]] + [72, [8, 48, 64]]
108 = [12, [6, 8, 10]] + [72, [8, 48, 64]] + [96, [19, 53, 90]]
36 = [18, [2, 12, 16]] + [24, [12, 16, 20]] + [30, [15, 20, 25]]
114 = [18, [2, 12, 16]] + [60, [21, 42, 51]] + [108, [12, 72, 96]]
123 = [18, [2, 12, 16]] + [96, [19, 53, 90]] + [99, [11, 66, 88]]
96 = [19, [3, 10, 18]] + [53, [29, 34, 44]] + [90, [10, 60, 80]]
82 = [19, [3, 10, 18]] + [60, [21, 42, 51]] + [69, [36, 38, 61]]
125 = [20, [7, 14, 17]] + [85, [50, 61, 64]] + [110, [29, 75, 96]]
108 = [24, [12, 16, 20]] + [38, [6, 20, 36]] + [106, [58, 68, 88]]
90 = [25, [4, 17, 22]] + [38, [6, 20, 36]] + [87, [20, 54, 79]]
54 = [27, [3, 18, 24]] + [36, [4, 24, 32]] + [45, [5, 30, 40]]
84 = [28, [18, 19, 21]] + [53, [29, 34, 44]] + [75, [12, 51, 66]]
110 = [29, [11, 15, 27]] + [75, [12, 51, 66]] + [96, [19, 53, 90]]
60 = [30, [15, 20, 25]] + [40, [14, 28, 34]] + [50, [8, 34, 44]]
56 = [36, [4, 24, 32]] + [38, [6, 20, 36]] + [42, [21, 28, 35]]
72 = [36, [4, 24, 32]] + [48, [24, 32, 40]] + [60, [21, 42, 51]]
84 = [42, [21, 28, 35]] + [56, [36, 38, 42]] + [70, [7, 54, 57]]
120 = [42, [21, 28, 35]] + [84, [28, 53, 75]] + [102, [51, 68, 85]]
116 = [44, [16, 23, 41]] + [60, [21, 42, 51]] + [108, [12, 72, 96]]
134 = [44, [16, 23, 41]] + [102, [51, 68, 85]] + [108, [12, 72, 96]]
90 = [45, [5, 30, 40]] + [60, [21, 42, 51]] + [75, [12, 51, 66]]
84 = [54, [6, 36, 48]] + [57, [9, 30, 54]] + [63, [7, 42, 56]]
108 = [54, [6, 36, 48]] + [72, [8, 48, 64]] + [90, [10, 60, 80]]
114 = [57, [9, 30, 54]] + [76, [12, 40, 72]] + [95, [15, 50, 90]]
120 = [60, [21, 42, 51]] + [80, [28, 56, 68]] + [100, [16, 68, 88]]
126 = [63, [7, 42, 56]] + [84, [28, 53, 75]] + [105, [33, 70, 92]]
132 = [66, [33, 44, 55]] + [88, [21, 43, 84]] + [110, [29, 75, 96]]
112 = [72, [8, 48, 64]] + [76, [12, 40, 72]] + [84, [28, 53, 75]]
138 = [81, [9, 54, 72]] + [90, [10, 60, 80]] + [111, [16, 47, 108]]
140 = [90, [10, 60, 80]] + [95, [15, 50, 90]] + [105, [33, 70, 92]]

Treenewbee

54 = [6, [3, 4, 5]] + [36, [4, 24, 32]] + [48, [24, 32, 40]]
     = [12, [6, 8, 10]] + [19, [3, 10, 18]] + [53, [29, 34, 44]]
     =[27, [3, 18, 24]] + [36, [4, 24, 32]] + [45, [5, 30, 40]]

Treenewbee

84 = [28, [18, 19, 21]] + [53, [29, 34, 44]] + [75, [12, 51, 66]]
     = [42, [21, 28, 35]] + [56, [36, 38, 42]] + [70, [7, 54, 57]]
     = [54, [6, 36, 48]] + [57, [9, 30, 54]] + [63, [7, 42, 56]]

Treenewbee

Treenewbee 发表于 2023-1-26 12:02
楼主所谓的完美立方数，太多了,如：

38 = [6, [3, 4, 5]] + [20, [7, 14, 17]] + [36, [4, 24, 32]]

一个简单的遍历判断而已。

蔡家雄

【完全数未解问题】6，28，496，8128，33550336，..........

求证：大于6的完全数各个数字之和，最终归于1.

28：2+8=10，1+0=1，
496：4+9+6=19，1+9=10，1+0=1，
8128：8+1+2+8=19，1+9=10，1+0=1，
33550336：3+3+5+5+0+3+3+6=28，2+8=10，1+0=1，

千年来：此问题悬而未决，但我早已找到该问题的巧妙的证法。

蔡家雄

【完全数-完美立方数】

设 M 是完全数，则 M=2^(p-1)*(2^p -1)，其中 (2^p -1) 是质数。

若 A^3=a1^3+a2^3+a3^3，B^3=b1^3+b2^3+b3^3，C^3=c1^3+c2^3+c3^3 均为正整数解，

及 D^3=d1^3+d2^3+d3^3，E^3=e1^3+e2^3+e3^3，F^3= f1^3+f2^3+f3^3 均为正整数解，

且 M^3=A^3+B^3+C^3=D^3+E^3+F^3

求 M= ？A= ?  B= ?  C= ?  D= ?  E= ?  F= ?

费尔马1

猜想，梅森素数无穷多，完全数（为偶数的）也无穷多。

太阳

蔡家雄 发表于 2023-1-25 13:24
【完全数-蔡氏质数猜想】

设 M 是完全数，则 M=2^(p-1)*(2^p -1)，其中 (2^p -1) 是质数。

逆命题是成立？1/k，( k为奇数)，具有最大循环节长k-1，判断k是素数？

太阳

蔡家雄 发表于 2023-1-26 17:21
【完全数-蔡氏质数猜想】

设 M 是完全数，则 M=2^(p-1)*(2^p -1)，其中 (2^p -1) 是质数。

逆命题是成立？1/(2^p-1)，( p为素数)，具有最大循环节长2^p-2，判断2^p-1是素数？
如果逆命题是正确，震惊世界

蔡家雄

判定梅森质数的卢卡斯序列

卢卡斯级数的通项公式

Ln=Round[((1+√3)/√2)^(2^n )/2]

L1=2,
L2=7,
L3=97,

L4=18817=(2^5 -1)(2^5*19 -1)=31*607,

并且：2^31 -1 与 2^607 -1 同为素数。

即有：2^30*(2^31 -1) 与 2^606*(2^607 -1) 都是 完全数。

L5=708158977,

L6=1002978273411373057

   =(2^7 -1)(2^7*61698958748239 -1)

   =127*7897466719774591,

已证：127 和 7897466719774591 都是素数，

已证：2^127 -1 是素数，据此 7897466719774591 是梅森素数，

即有：2^126*(2^127 -1) 是完全数，

以及：2^7897466719774590*(2^7897466719774591 -1) 是 完全数。