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Diophantine equation with squares and powers of 17

Source: 2021 Junior Macedonian Mathematical Olympiad P3

June 8, 2021
number theoryDiophantine equation

Problem Statement

Find all positive integers nn and prime numbers pp such that 17n⋅2n2−p=(2n2+3+2n2−1)⋅n2.17^n \cdot 2^{n^2} - p =(2^{n^2+3}+2^{n^2}-1) \cdot n^2.
Proposed by Nikola Velov
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