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Polynomials are prime numbers

Source: 2020 1st OMpD L2 P3 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
algebrapolynomialnumber theoryprime numbers

Problem Statement

Determine all integers nn such that both of the numbers: ∣n3−4n2+3n−35∣ and ∣n2+4n+8∣|n^3 - 4n^2 + 3n - 35| \text{ and } |n^2 + 4n + 8| are both prime numbers.
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