RIOPLATENSE 2000 Problem 4

Let $a, b$ and $c$ be positive integers such that $a^2 + b^2 + 1 = c^2$ . Prove that $[a/2] + [c / 2]$ is even.

Note: $[x]$ is the integer part of $x$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.