Problem 135
Same differences
Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer, n, for which the equation, x2 − y2 − z2 = n, has exactly two solutions is n = 27:
It turns out that n = 1155 is the least value which has exactly ten solutions.
How many values of n less than one million have exactly ten distinct solutions?
相同的差
已知正整数x，y，z构成等差数列，使得方程x2 − y2 − z2 = n有两个解的最小正整数为n=27：
使得方程有十个解的最小正整数为n = 1155。
在小于一百万的数中，有多少个n的取值使得方程恰好有十个不同的解？