IMO 2023 Shortlist N4
Let a1,a2,...,an,b1,b2,...,bn be 2n positive integers such that the n 1 products a1a2a3 ¨¨¨an, b1a2a3 ¨¨¨an, b1b2a3 ¨¨¨a...
Category: Number Theory
Problem
Let a1,a2,...,an,b1,b2,...,bn be 2n positive integers such that the n ` 1 products a1a2a3 ¨¨¨an, b1a2a3 ¨¨¨an, b1b2a3 ¨¨¨an, . . . b1b2b3 ¨¨¨bn form a strictly increasing arithmetic progression in that order. Determine the smallest positive integer that could be the common difference of such an arithmetic progression. (Canada)