让MMA求出某类不定方程的通解？

青青子衿

MMA能求出三元二次不定方程的特解，如何求出三元二次不定方程的通解呢？
如何编写算法，让MMA求出三元二次不定方程的通解

1. Solve[x^2 + 7 y^2 == z^2 && 0 < x < 100 && 0 < y < 100 &&
2.   0 < z < 100 && GCD[x, y, z] == 1, {x, y, z}, Integers]

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The general solution to x^2 + 7y^2 = z^2 is:

x = a^2 - 7b^2
y = 2ab
z = a^2 + 7b^2

where a and b are integers.