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Sum of factorials is a square

Source: 2022 Grosman Mathematical Olympiad P1

September 22, 2022
factorialnumber theory

Problem Statement

For each positive integer nn denote: n!=1⋅2⋅3…nn!=1\cdot 2\cdot 3\dots n Find all positive integers nn for which 1!+2!+3!+⋯+n!1!+2!+3!+\cdots+n! is a perfect square.
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