Problem 136
Singleton difference
The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2 − y2 − z2 = n, has exactly one solution when n = 20:
In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.
How many values of n less than fifty million have exactly one solution?
唯一的差
正整数x，y，z构成等差数列。取正整数n=20，此时方程x2 − y2 − z2 = n只有一个解：
事实上，在小于一百的数中，有25个n的取值使得方程有唯一解。
在小于五千万的数中，有多少个n的取值使得方程有唯一解？