>

> When in doubt, Generalize.

> p^2 + q^2 - b^2 = k^2 has infinite solutions for b prime, b*p>3 p prime and no solutions for b a multiple of 4 or 6, maybe finite solutions b = p*3 or p*2, p prime.

> El Cino

>

Generalizing to the n-th degree, with a touch of Serendipity,

1. p^n + q^n - b^n = k^2 has no integer solutions b, k for p, q prime, n odd > 3.

For p,q not both prime, there are many solutions.

p^n + q^n - b^n = k^m odd n > 3 has solutions but they are trivial, p, q = b.

Maybe someone can prove 1.

Cino

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