Question 59
a) What is the smallest positive integer $c$ for which there exists at least one pair $(a, b)$ of distinct positive integers such that $2 c^{2} = a^{2} + b^{2}$?
b) Prove that there exist infinitely many triples $(a, b, c)$ of distinct positive integers such that $2 c^{2} = a^{2} + b^{2}$.
b) Prove that there exist infinitely many triples $(a, b, c)$ of distinct positive integers such that $2 c^{2} = a^{2} + b^{2}$.