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4

Part of 2020 Regional Olympiad of Mexico Northeast

Problems(1)

4p-3 is perfect square if n |(p-1) and p|(n^3-1)

Source: Mathematics Regional Olympiad of Mexico Northeast 2020 P4

9/7/2022
Let n>1n > 1 be an integer and pp be a prime. Prove that if n∣p−1n|p-1 and p∣n3−1p|n^3-1, then 4p−34p-3 is a perfect square.
number theorydividesprimePerfect Square