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a(a+1)(a+2) ...(a+2023) divides b(b+1)...(b+2023)

Source: P4 Francophone Math Olympiad Senior 2023

May 2, 2023
number theorydividesconsecutiveProduct

Problem Statement

Do there exist integers aa and bb such that none of the numbers a,a+1,…,a+2023,b,b+1,…,b+2023a,a+1,\ldots,a+2023,b,b+1,\ldots,b+2023 divides any of the 40474047 other numbers, but a(a+1)(a+2)⋯(a+2023)a(a+1)(a+2)\cdots(a+2023) divides b(b+1)⋯(b+2023)b(b+1)\cdots(b+2023)?
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