Problem

Source: Romania TST 2015 Day 1 Problem 3

Tags: number theory, Romanian TST, induction



A Pythagorean triple is a solution of the equation $x^2 + y^2 = z^2$ in positive integers such that $x < y$. Given any non-negative integer $n$ , show that some positive integer appears in precisely $n$ distinct Pythagorean triples.