排列组合Aquadruple(a,b,c,d)ofpositiveintegerssuchthata≤b≤c≤da,b,c,dareconsecutivetermsinanarithmeticsequencea^3+b^3+c^3=d^3atleastoneofa,b,c,dbetween1867and2008inclusive.Iscalleda

Question

排列组合
A quadruple (a,b,c,d) of positive integers such that
 a≤b≤c≤d
 a,b,c,d are consecutive terms in an arithmetic sequence
 a^3+b^3+c^3=d^3
 at least one of a,b,c,d between 1867 and 2008 inclusive.
Is called a quixotic quadruple.How many quixotic quadruples are there?
是一个比赛上的题，如果你找到了能把解法发给我吗？
题目大概是这个意思，abcd四个正整数，a≤b≤c≤d;a^3+b^3+c^3=d^3;a,b,c,d是等差数列;a,b,c,d中至少有一个是在1867和2008之间的。问一共用多少种可能的abcd组合。

Answer 1

太难了,没看懂啊