Number theory · Perfect squares · Explicit construction · Parity · Mathematical induction · Pythagorean triples
Prove that for every integer \(n \geqslant 2\) one can find \(n\) pairwise distinct positive integers whose squares add up to the square of a positive integer.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 2003, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source