Number theory · Difference of squares · Parity · Residues mod 4
Let \(a\) and \(b\) be natural numbers. Prove that natural numbers \(c\) and \(d\) with
\[ a^2 + b^2 + c^2 = d^2 \]
exist if and only if at least one of the numbers \(a\) and \(b\) is even.
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Serbian Regional Competition (Okruzno takmicenje) 2015, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source