a^3=0,1,8,27,64,・・・

1,2,9,28,65,

8,9,16,35,72

27,28,35,54,91

64,65,72,91,128

a^3+b^3=0,1,2,8,9,16,27,28,35,54,64,65,72,91,・・・

これに対しては15定理は成立しない。

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

0,1,2,8,9,16,27,28,35,54,64,65,72,91,・・・

1,2,3,9,10,17,28,29,36,55,65,66,73,92,・・・

8,9,16,17,24,35,36,43,62,72,73,80,99,・・・

27,28,29,36,43,54,55,84,・・・

64,65,66,72,73,80,91,92,99,・・・

a^3+b^3+c^3=0,1,2,3,8,9,10,16,17,24,27,28,29,35,36,43,54,55,62,64,65,66,72,73,80,84,91,92,99,・・・

ある整数を３乗した数（立方数）を三つ，足したり引いたりしてNを作る問題には，4,5,13,14,22,23のように，９で割って余りが４か５になる数には答えがないこともわかっている．

x=0,1,2,3,4,5,6,7,8(mod9)に対して

x^3=0,1,-1,0,1,-1,0,1,-1

x^3+y3+z^3=0,1,2,3,-1,-2,-3

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

0,1,2,3,8,9,10,16,17,24,27,28,29,35,36,43,54,55,62,64,65,66,72,73,80,84,91,92,99,・・・

1,2,3,4,9,10,11,17,18,25,28,29,30,36,37,44,55,56,63,65,66,67,73,74,81,85,92,93,99,

8,9,10,11,16,17,18,24,25,32,35,36,37,43,44,51,62,63,70,72,73,74,80,81,88,92,99,100,・・・

27,28,29,30,35,36,37,43,44,51,54,55,56,62,63,70,81,82,89,91,92,93,99,100,・・・

64,65,66,67,72,73,74,80,81,88,91,92,93,99,100,・・・

a^3+b^3+c^3+d^3

0,1,2,3,4,8,9,10,11,16,17,18,24,25,27,28,29,30,32,35,36,37,43,44,51,54,55,56,62,63,64,65,66,67,70,72,73,74,80,81,82,84,85,89,91,92,93,99,100,・・

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

0,1,2,3,4,8,9,10,11,16,17,18,24,25,27,28,29,30,32,35,36,37,43,44,51,54,55,56,62,63,64,65,66,67,70,72,73,74,80,81,82,84,85,89,91,92,93,99,100,・・

1,2,3,4,5,9,10,11,12,17,18,19,25,26,28,29,30,31,33,36,37,38,44,45,52,55,56,57,63,64,65,66,67,68,71,73,74,75,81,82,83,85,86,90,92,93,94,100,・・

8,9,10,11,12,16,17,18,19,24,25,26,32,33,35,36,37,38,40,43,44,45,51,52,59,62,63,64,70,71,72,73,74,75,78,80,81,82,88,89,90,92,93,97,99,100,・・

27,28,29,30,31,35,36,37,38,43,44,45,51,52,54,55,56,57,59,62,63,64,70,71,78,81,82,83,89,90,91,92,93,94,97,99,100,・・

64,65,66,67,68,72,73,74,75,80,81,82,88,89,91,92,93,94,96,99,100,・・

a^3+b^3+c^3+d^3+e^3

0,1,2,3,4,5,8,9,10,11,12,16,17,18,19,24,25,26,27,28,29,30,31,32,33,35,36,37,38,40,43,44,45,51,52,54,55,56,57,59,62,63,64,65,66,67,68,70,71,72,73,74,75,78,80,81,82,83,84,85,86,88,89,90,91,92,93,94,96,97,99,100,・・

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

0,1,2,3,4,5,8,9,10,11,12,16,17,18,19,24,25,26,27,28,29,30,31,32,33,35,36,37,38,40,43,44,45,51,52,54,55,56,57,59,62,63,64,65,66,67,68,70,71,72,73,74,75,78,80,81,82,83,84,85,86,88,89,90,91,92,93,94,96,97,99,100,・・

1,2,3,4,5,6,9,10,11,12,13,17,18,19,20,25,26,27,28,29,30,31,32,33,34,36,37,38,39,41,44,45,46,52,53,55,56,57,58,60,63,64,65,66,67,68,69,71,72,73,74,75,76,79,81,82,83,84,85,86,87,89,90,91,92,93,94,95,97,98,100,・・

8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,31,32,34,35,36,37,38,39,40,41,43,44,45,46,48,51,52,53,59,60,62,63,64,65,67,70,71,72,73,74,75,76,78,79,80,81,82,83,84,88,89,90,91,92,93,94,96,97,98,99,100,・・

27,28,29,30,31,32,35,36,37,38,39,43,44,45,46,51,52,53,54,55,56,57,58,59,60,62,63,64,65,67,70,71,72,78,79,81,82,83,84,86,89,90,91,92,93,94,65,97,798,99,100,・・

a^3+b^3+c^3+d^3+e^3+f^3

0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43,44,45,46,48,51,52,53,54,55,56,57,58,59,60,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,78,79,80,81,82,83,84,85,86,88,89,90,91,92,93,94,95,96,97,98,99,100,・・

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝