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Mod 3

Age 14 to 16 Challenge Level:

Prove that if $a^2+b^2$ is a multiple of $3$ then both $a$ and $b$ are multiples of $3$.

Modular arithmetic. Inequalities. Number theory. Creating and manipulating expressions and formulae. Divisibility. Mathematical reasoning & proof. Mathematical induction. Indices. Number - generally. Factors and multiples.