MathDB

1

Part of 2022 Irish Math Olympiad

Problems(1)

n!+3 equaling a power of 3

Source: IrMO 2022

5/8/2022
1. For n a positive integer, n! = 1 ⋅\cdot 2 ⋅\cdot 3 …\dots (n - 1) ⋅\cdot n is the product of the positive integers from 1 to n.
Determine, with proof, all positive integers n for which n! + 3 is a power of 3.
number theoryfactorial