PUMaC 2024 · 数论（A 组） · 第 7 题

PUMaC 2024 — Number Theory (Division A) — Problem 7

Call a 2-by-2 grid a perfectly perfect square if it contains distinct positive integers such that the sum of each row is a perfect square and the sum of each column is a perfect square. Define f ( n ) to be the number of perfectly perfect squares whose entries sum to n . Let m be the smallest integer such that f ( m ) > m . Find f ( m ). 1 1 1 N

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