Stage: 4 Challenge Level: 
Prove that if $a^2+b^2$ is a multiple of $3$ then both $a$ and $b$ are multiples of $3$.
Manipulating algebraic expressions/formulae. Modulus arithmetic. Divisibility. Mathematical reasoning & proof. Generalising. Number - generally. Number theory. Inequality/inequalities. Stage 5 - Reviewed 2012. Factors and multiples.
Published July 2001.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk