Number theory · Sums of two squares · Parity · Algebraic identities
Prove that a natural number of the form \(4n + 1\) can be represented as a sum of two squares if and only if the number \(8n + 2\) can be represented as a sum of two squares.
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Serbian Municipal Competition 1999, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source