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MathNet 2026 — Part 09 Question 181

Math Olympiad Vault · MathNet 2026 — Part 09

Question 181

Let $n$ be a positive integer which is divisible by $5$ and which can be written as the sum of two (not necessarily distinct) squares. Prove that $n$ can be written as the sum of two squares one of which is greater than or equal to four times the other.