On primitive solutions of the Diophantine equation x2 + y2 = M

Abstract

We provide explicit formulae for primitive, integral solutions to the Diophantine equation x2+y2=M{x}^{2}+{y}^{2}=M, where MM is a product of powers of Pythagorean primes, i.e., of primes of the form 4n+14n+1. It turns out that this is a nice application of the theory of Gaussian integers.

Keywords

• pythagorean primes
• diophantine equation
• 11d45
• 11d09
• 11a41