CUBES - Perfect Cubes

题意翻译

给出方程 $a^3=b^3+c^3+d^3$ 写一个程序来找出满足这个方程的所有的数字集合${a(a\le 100),b,c,d}$,每一个集合只需要输出**一种组合**即可。 这是程序的一部分输出: ``` Cube = 6, Triple = (3,4,5) Cube = 12, Triple = (6,8,10) Cube = 18, Triple = (2,12,16) Cube = 18, Triple = (9,12,15) Cube = 19, Triple = (3,10,18) Cube = 20, Triple = (7,14,17) Cube = 24, Triple = (12,16,20) ```

题目描述

For hundreds of years Fermat's Last Theorem, which stated simply that for _n_ > 2 there exist no integers _a_, _b_, _c_ > 1 such that _a_^_n_ = _b_^_n_ + _c_^_n_, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It _is_ possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation _a_^3 = _b_^3 + _c_^3 + _d_^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {_a_,_b_,_c_,_d_} which satisfy this equation for _a_ <= 100. The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their _a_ values). The values of _b_, _c_, and _d_ should also be listed in non-decreasing order on the line itself. There do exist several values of _a_ which can be produced from multiple distinct sets of _b_, _c_, and _d_ triples. In these cases, the triples with the smaller _b_ values should be listed first. Note that the programmer will need to be concerned with an efficient implementation. The official time limit for this problem is 2 minutes, and it is indeed possible to write a solution to this problem which executes in under 2 minutes on a 33 MHz 80386 machine. Due to the distributed nature of the contest in this region, judges have been instructed to make the official time limit at their site the greater of 2 minutes or twice the time taken by the judge's solution on the machine being used to judge this problem. The first part of the output is shown here: ``` Cube = 6, Triple = (3,4,5) Cube = 12, Triple = (6,8,10) Cube = 18, Triple = (2,12,16) Cube = 18, Triple = (9,12,15) Cube = 19, Triple = (3,10,18) Cube = 20, Triple = (7,14,17) Cube = 24, Triple = (12,16,20) ```

输入输出格式

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输入输出样例

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