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P1

Part of 2022 Grosman Mathematical Olympiad

Problems(1)

Sum of factorials is a square

Source: 2022 Grosman Mathematical Olympiad P1

9/22/2022
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.
factorialnumber theory