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divisibility with primes

Source: Mathematics Regional Olympiad of Mexico Southeast 2019 P6

October 23, 2021
number theoryprime numbers

Problem Statement

Let p≥3p\geq 3 a prime number, aa and bb integers such that gcd⁡(a,b)=1\gcd(a, b)=1. Let nn a natural number such that pp divides a2n+b2na^{2^n}+b^{2^n}, prove that 2n+12^{n+1} divides p−1p-1.
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