离死亡还有 往生已逝的放废话的空间 20101206

往生已逝的放废话的空间

往生已逝のゴミ言葉箱【心跳回忆百科全书建设中】

数学的扭曲

起因是matrix67他在推上写:

RT@matrix67 Gu Sen 不要以为 n 越小就越容易解决。把一个数表示成三个立方数之和,则 5256 = 11^3 + 12^3 + 13^3,但 2 = 1214928^3 + 3480205^3 + (-3528875)^3

我没有演算就信以为真的放上去了
友人core阅毕存疑,寻找最优解
少顷得出:

 2 = -5^3 + -6^3 + 7^3 wwwwww

嗯感谢指正。
以下的计算的程序与结果记录均为core所做
设a=x^3+y^3+z^3,xyz均取-100~100的整数,设定a在0~100内时,有多少组xyz有解。
顺便一提结论相当惊人,有近2/3的0~100的数字可以用三个-100~100的立方和表述。
此外我对“不可表述的数字”几乎都是连串出现这一现象很有兴趣
寻找最优解过程如下,

一 未改良算法 23秒 -100~100穷举
0 = cube(-100) + cube(0) + cube(100)
1 = cube(-100) + cube(1) + cube(100)
2 = cube(-47) + cube(-24) + cube(49)
No result found for 3 when x, y, z E [-100, 100].
No result found for 4 when x, y, z E [-100, 100].
No result found for 5 when x, y, z E [-100, 100].
6 = cube(-58) + cube(-43) + cube(65)
7 = cube(-1) + cube(0) + cube(2)
8 = cube(-100) + cube(2) + cube(100)
9 = cube(0) + cube(1) + cube(2)
No result found for 10 when x, y, z E [-100, 100].
No result found for 11 when x, y, z E [-100, 100].
12 = cube(-11) + cube(7) + cube(10)
No result found for 13 when x, y, z E [-100, 100].
No result found for 14 when x, y, z E [-100, 100].
15 = cube(-46) + cube(23) + cube(44)
16 = cube(-94) + cube(-48) + cube(98)
17 = cube(-52) + cube(25) + cube(50)
18 = cube(-2) + cube(-1) + cube(3)
19 = cube(-95) + cube(47) + cube(91)
20 = cube(-56) + cube(21) + cube(55)
21 = cube(-86) + cube(28) + cube(85)
No result found for 22 when x, y, z E [-100, 100].
No result found for 23 when x, y, z E [-100, 100].
No result found for 24 when x, y, z E [-100, 100].
No result found for 25 when x, y, z E [-100, 100].
26 = cube(-1) + cube(0) + cube(3)
27 = cube(-100) + cube(3) + cube(100)
28 = cube(-59) + cube(31) + cube(56)
29 = cube(-20) + cube(13) + cube(18)
No result found for 30 when x, y, z E [-100, 100].
No result found for 31 when x, y, z E [-100, 100].
No result found for 32 when x, y, z E [-100, 100].
No result found for 33 when x, y, z E [-100, 100].
34 = cube(-4) + cube(-3) + cube(5)
35 = cube(-13) + cube(-8) + cube(14)
36 = cube(-75) + cube(40) + cube(71)
37 = cube(-56) + cube(37) + cube(50)
38 = cube(-27) + cube(16) + cube(25)
No result found for 39 when x, y, z E [-100, 100].
No result found for 40 when x, y, z E [-100, 100].
No result found for 41 when x, y, z E [-100, 100].
No result found for 42 when x, y, z E [-100, 100].
43 = cube(-52) + cube(20) + cube(51)
44 = cube(-7) + cube(-5) + cube(8)
45 = cube(-3) + cube(2) + cube(4)
46 = cube(-29) + cube(19) + cube(26)
47 = cube(-30) + cube(-14) + cube(31)
48 = cube(-26) + cube(-23) + cube(31)
No result found for 49 when x, y, z E [-100, 100].
No result found for 50 when x, y, z E [-100, 100].
No result found for 51 when x, y, z E [-100, 100].
No result found for 52 when x, y, z E [-100, 100].
53 = cube(-4) + cube(-2) + cube(5)
54 = cube(-18) + cube(-15) + cube(21)
55 = cube(-9) + cube(-6) + cube(10)
56 = cube(-47) + cube(31) + cube(42)
57 = cube(-38) + cube(25) + cube(34)
No result found for 58 when x, y, z E [-100, 100].
No result found for 59 when x, y, z E [-100, 100].
60 = cube(-4) + cube(-1) + cube(5)
61 = cube(-4) + cube(0) + cube(5)
62 = cube(-43) + cube(22) + cube(41)
63 = cube(-63) + cube(-37) + cube(67)
64 = cube(-100) + cube(4) + cube(100)
65 = cube(0) + cube(1) + cube(4)
No result found for 66 when x, y, z E [-100, 100].
No result found for 67 when x, y, z E [-100, 100].
No result found for 68 when x, y, z E [-100, 100].
69 = cube(-22) + cube(-19) + cube(26)
70 = cube(-64) + cube(23) + cube(63)
71 = cube(-33) + cube(-22) + cube(36)
72 = cube(-27) + cube(-13) + cube(28)
73 = cube(-47) + cube(29) + cube(43)
No result found for 74 when x, y, z E [-100, 100].
No result found for 75 when x, y, z E [-100, 100].
No result found for 76 when x, y, z E [-100, 100].
No result found for 77 when x, y, z E [-100, 100].
78 = cube(-55) + cube(26) + cube(53)
79 = cube(-66) + cube(-49) + cube(74)
No result found for 80 when x, y, z E [-100, 100].
81 = cube(-18) + cube(10) + cube(17)
No result found for 82 when x, y, z E [-100, 100].
83 = cube(-36) + cube(-32) + cube(43)
No result found for 84 when x, y, z E [-100, 100].
No result found for 85 when x, y, z E [-100, 100].
No result found for 86 when x, y, z E [-100, 100].
No result found for 87 when x, y, z E [-100, 100].
88 = cube(-16) + cube(-9) + cube(17)
No result found for 89 when x, y, z E [-100, 100].
90 = cube(-100) + cube(31) + cube(99)
91 = cube(-5) + cube(0) + cube(6)
92 = cube(-8) + cube(-5) + cube(9)
No result found for 93 when x, y, z E [-100, 100].
No result found for 94 when x, y, z E [-100, 100].
No result found for 95 when x, y, z E [-100, 100].
96 = cube(-22) + cube(14) + cube(20)
97 = cube(-22) + cube(17) + cube(18)
98 = cube(-15) + cube(9) + cube(14)
99 = cube(-37) + cube(16) + cube(36)
100 = cube(-6) + cube(-3) + cube(7)
Total 59 valid numbers in [0, 100].
Press any key to continue . . . 

二 改良算法 从0~绝对值100穷举 耗时9秒
0 = cube(0) + cube(1) + cube(-1)
1 = cube(1) + cube(2) + cube(-2)
2 = cube(-5) + cube(7) + cube(-6)
No result found for 3 when x, y, z E [-100, 100].
No result found for 4 when x, y, z E [-100, 100].
No result found for 5 when x, y, z E [-100, 100].
6 = cube(-43) + cube(65) + cube(-58)
7 = cube(0) + cube(2) + cube(-1)
8 = cube(1) + cube(-1) + cube(2)
9 = cube(0) + cube(1) + cube(2)
No result found for 10 when x, y, z E [-100, 100].
No result found for 11 when x, y, z E [-100, 100].
12 = cube(7) + cube(10) + cube(-11)
No result found for 13 when x, y, z E [-100, 100].
No result found for 14 when x, y, z E [-100, 100].
15 = cube(23) + cube(44) + cube(-46)
16 = cube(-10) + cube(14) + cube(-12)
17 = cube(25) + cube(50) + cube(-52)
18 = cube(-1) + cube(3) + cube(-2)
19 = cube(0) + cube(3) + cube(-2)
20 = cube(1) + cube(3) + cube(-2)
21 = cube(-11) + cube(16) + cube(-14)
No result found for 22 when x, y, z E [-100, 100].
No result found for 23 when x, y, z E [-100, 100].
No result found for 24 when x, y, z E [-100, 100].
No result found for 25 when x, y, z E [-100, 100].
26 = cube(0) + cube(3) + cube(-1)
27 = cube(1) + cube(-1) + cube(3)
28 = cube(0) + cube(1) + cube(3)
29 = cube(-2) + cube(4) + cube(-3)
No result found for 30 when x, y, z E [-100, 100].
No result found for 31 when x, y, z E [-100, 100].
No result found for 32 when x, y, z E [-100, 100].
No result found for 33 when x, y, z E [-100, 100].
34 = cube(-1) + cube(2) + cube(3)
35 = cube(0) + cube(2) + cube(3)
36 = cube(1) + cube(2) + cube(3)
37 = cube(0) + cube(4) + cube(-3)
38 = cube(1) + cube(4) + cube(-3)
No result found for 39 when x, y, z E [-100, 100].
No result found for 40 when x, y, z E [-100, 100].
No result found for 41 when x, y, z E [-100, 100].
No result found for 42 when x, y, z E [-100, 100].
43 = cube(8) + cube(12) + cube(-13)
44 = cube(-5) + cube(8) + cube(-7)
45 = cube(2) + cube(4) + cube(-3)
46 = cube(19) + cube(26) + cube(-29)
47 = cube(6) + cube(7) + cube(-8)
48 = cube(-23) + cube(31) + cube(-26)
No result found for 49 when x, y, z E [-100, 100].
No result found for 50 when x, y, z E [-100, 100].
No result found for 51 when x, y, z E [-100, 100].
No result found for 52 when x, y, z E [-100, 100].
53 = cube(-2) + cube(5) + cube(-4)
54 = cube(-7) + cube(12) + cube(-11)
55 = cube(-1) + cube(4) + cube(-2)
56 = cube(0) + cube(4) + cube(-2)
57 = cube(1) + cube(4) + cube(-2)
No result found for 58 when x, y, z E [-100, 100].
No result found for 59 when x, y, z E [-100, 100].
60 = cube(-1) + cube(5) + cube(-4)
61 = cube(0) + cube(5) + cube(-4)
62 = cube(1) + cube(5) + cube(-4)
63 = cube(0) + cube(4) + cube(-1)
64 = cube(1) + cube(-1) + cube(4)
65 = cube(0) + cube(1) + cube(4)
No result found for 66 when x, y, z E [-100, 100].
No result found for 67 when x, y, z E [-100, 100].
No result found for 68 when x, y, z E [-100, 100].
69 = cube(2) + cube(5) + cube(-4)
70 = cube(11) + cube(20) + cube(-21)
71 = cube(-1) + cube(2) + cube(4)
72 = cube(0) + cube(2) + cube(4)
73 = cube(1) + cube(2) + cube(4)
No result found for 74 when x, y, z E [-100, 100].
No result found for 75 when x, y, z E [-100, 100].
No result found for 76 when x, y, z E [-100, 100].
No result found for 77 when x, y, z E [-100, 100].
78 = cube(26) + cube(53) + cube(-55)
79 = cube(-19) + cube(35) + cube(-33)
No result found for 80 when x, y, z E [-100, 100].
81 = cube(10) + cube(17) + cube(-18)
No result found for 82 when x, y, z E [-100, 100].
83 = cube(-2) + cube(3) + cube(4)
No result found for 84 when x, y, z E [-100, 100].
No result found for 85 when x, y, z E [-100, 100].
No result found for 86 when x, y, z E [-100, 100].
No result found for 87 when x, y, z E [-100, 100].
88 = cube(3) + cube(5) + cube(-4)
No result found for 89 when x, y, z E [-100, 100].
90 = cube(-1) + cube(3) + cube(4)
91 = cube(0) + cube(3) + cube(4)
92 = cube(1) + cube(3) + cube(4)
No result found for 93 when x, y, z E [-100, 100].
No result found for 94 when x, y, z E [-100, 100].
No result found for 95 when x, y, z E [-100, 100].
96 = cube(14) + cube(20) + cube(-22)
97 = cube(-1) + cube(5) + cube(-3)
98 = cube(0) + cube(5) + cube(-3)
99 = cube(1) + cube(5) + cube(-3)
100 = cube(-3) + cube(7) + cube(-6)
Total 59 valid numbers in [0, 100].
Completed in 9 s.

三 排除三个数中有两数绝对值相同的情况
所谓平凡解指的是正负绝对值相同的两数,其立方和也为0,因此立方数如27就有很多组平凡解。
因此计算非平凡解的结果是
除了0根据费马大定理理所当然的被排除掉后,其他的全部存活
No result found for 0 when x, y, z E [-100, 100].
1 = cube(-6) + cube(9) + cube(-8)
2 = cube(-5) + cube(7) + cube(-6)
No result found for 3 when x, y, z E [-100, 100].
No result found for 4 when x, y, z E [-100, 100].
No result found for 5 when x, y, z E [-100, 100].
6 = cube(-43) + cube(65) + cube(-58)
7 = cube(0) + cube(2) + cube(-1)
8 = cube(9) + cube(15) + cube(-16)
9 = cube(0) + cube(1) + cube(2)
No result found for 10 when x, y, z E [-100, 100].
No result found for 11 when x, y, z E [-100, 100].
12 = cube(7) + cube(10) + cube(-11)
No result found for 13 when x, y, z E [-100, 100].
No result found for 14 when x, y, z E [-100, 100].
15 = cube(23) + cube(44) + cube(-46)
16 = cube(-10) + cube(14) + cube(-12)
17 = cube(25) + cube(50) + cube(-52)
18 = cube(-1) + cube(3) + cube(-2)
19 = cube(0) + cube(3) + cube(-2)
20 = cube(1) + cube(3) + cube(-2)
21 = cube(-11) + cube(16) + cube(-14)
No result found for 22 when x, y, z E [-100, 100].
No result found for 23 when x, y, z E [-100, 100].
No result found for 24 when x, y, z E [-100, 100].
No result found for 25 when x, y, z E [-100, 100].
26 = cube(0) + cube(3) + cube(-1)
27 = cube(-4) + cube(6) + cube(-5)
28 = cube(0) + cube(1) + cube(3)
29 = cube(-2) + cube(4) + cube(-3)
No result found for 30 when x, y, z E [-100, 100].
No result found for 31 when x, y, z E [-100, 100].
No result found for 32 when x, y, z E [-100, 100].
No result found for 33 when x, y, z E [-100, 100].
34 = cube(-1) + cube(2) + cube(3)
35 = cube(0) + cube(2) + cube(3)
36 = cube(1) + cube(2) + cube(3)
37 = cube(0) + cube(4) + cube(-3)
38 = cube(1) + cube(4) + cube(-3)
No result found for 39 when x, y, z E [-100, 100].
No result found for 40 when x, y, z E [-100, 100].
No result found for 41 when x, y, z E [-100, 100].
No result found for 42 when x, y, z E [-100, 100].
43 = cube(8) + cube(12) + cube(-13)
44 = cube(-5) + cube(8) + cube(-7)
45 = cube(2) + cube(4) + cube(-3)
46 = cube(19) + cube(26) + cube(-29)
47 = cube(6) + cube(7) + cube(-8)
48 = cube(-23) + cube(31) + cube(-26)
No result found for 49 when x, y, z E [-100, 100].
No result found for 50 when x, y, z E [-100, 100].
No result found for 51 when x, y, z E [-100, 100].
No result found for 52 when x, y, z E [-100, 100].
53 = cube(-2) + cube(5) + cube(-4)
54 = cube(-7) + cube(12) + cube(-11)
55 = cube(-1) + cube(4) + cube(-2)
56 = cube(0) + cube(4) + cube(-2)
57 = cube(1) + cube(4) + cube(-2)
No result found for 58 when x, y, z E [-100, 100].
No result found for 59 when x, y, z E [-100, 100].
60 = cube(-1) + cube(5) + cube(-4)
61 = cube(0) + cube(5) + cube(-4)
62 = cube(1) + cube(5) + cube(-4)
63 = cube(0) + cube(4) + cube(-1)
64 = cube(-3) + cube(6) + cube(-5)
65 = cube(0) + cube(1) + cube(4)
No result found for 66 when x, y, z E [-100, 100].
No result found for 67 when x, y, z E [-100, 100].
No result found for 68 when x, y, z E [-100, 100].
69 = cube(2) + cube(5) + cube(-4)
70 = cube(11) + cube(20) + cube(-21)
71 = cube(-1) + cube(2) + cube(4)
72 = cube(0) + cube(2) + cube(4)
73 = cube(1) + cube(2) + cube(4)
No result found for 74 when x, y, z E [-100, 100].
No result found for 75 when x, y, z E [-100, 100].
No result found for 76 when x, y, z E [-100, 100].
No result found for 77 when x, y, z E [-100, 100].
78 = cube(26) + cube(53) + cube(-55)
79 = cube(-19) + cube(35) + cube(-33)
No result found for 80 when x, y, z E [-100, 100].
81 = cube(10) + cube(17) + cube(-18)
No result found for 82 when x, y, z E [-100, 100].
83 = cube(-2) + cube(3) + cube(4)
No result found for 84 when x, y, z E [-100, 100].
No result found for 85 when x, y, z E [-100, 100].
No result found for 86 when x, y, z E [-100, 100].
No result found for 87 when x, y, z E [-100, 100].
88 = cube(3) + cube(5) + cube(-4)
No result found for 89 when x, y, z E [-100, 100].
90 = cube(-1) + cube(3) + cube(4)
91 = cube(0) + cube(3) + cube(4)
92 = cube(1) + cube(3) + cube(4)
No result found for 93 when x, y, z E [-100, 100].
No result found for 94 when x, y, z E [-100, 100].
No result found for 95 when x, y, z E [-100, 100].
96 = cube(14) + cube(20) + cube(-22)
97 = cube(-1) + cube(5) + cube(-3)
98 = cube(0) + cube(5) + cube(-3)
99 = cube(1) + cube(5) + cube(-3)
100 = cube(-3) + cube(7) + cube(-6)
Total 58 valid numbers in [0, 100].
Completed in 11 s.

四 排除三个数中有两数绝对值相同的情况 穷举所有结果
提出这个问题,是因为我想看看1-100的数字的非平凡解是哪个数字最多


此问题待续

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