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cubefree divisibility

Source: 2021 ISL N1

July 12, 2022
number theoryIMO ShortlistDivisibilitycubefreeHi

Problem Statement

Find all positive integers n≥1n\geq1 such that there exists a pair (a,b)(a,b) of positive integers, such that a2+b+3a^2+b+3 is not divisible by the cube of any prime, and n=ab+3b+8a2+b+3.n=\frac{ab+3b+8}{a^2+b+3}.
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