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Divisibility with 2024 integers

Source: ICMC 7 Round 2 Problem 1

March 12, 2024

number theory

Problem Statement

Prove that there exist distinct positive integers

a_1, a_2,\ldots , a_{2024}

such that for each

i\in\{1,2,\ldots,2024\}

a_i\mid a_1a_2\cdots a_{i-1}a_{i+1}\cdots a_{2024}+k,

where a)

k=1

and b)

k=2024.

Proposed by Ishan Nath

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