MathDB

N4

Part of 2023 ISL

Problems(1)

Arithmetic Sequence of Products

Source: IMO Shortlist 2023 N4

7/17/2024
Let a1,…,an,b1,…,bna_1, \dots, a_n, b_1, \dots, b_n be 2n2n positive integers such that the n+1n+1 products a1a2a3⋯an,b1a2a3⋯an,b1b2a3⋯an,…,b1b2b3⋯bna_1 a_2 a_3 \cdots a_n, b_1 a_2 a_3 \cdots a_n, b_1 b_2 a_3 \cdots a_n, \dots, b_1 b_2 b_3 \cdots b_n form a strictly increasing arithmetic progression in that order. Determine the smallest possible integer that could be the common difference of such an arithmetic progression.
arithmetic sequencenumber theory