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Problem 327

AMC 12 late, AIME early

Number theory Difficulty 4.7 Find the answer

9.1. Find all prime numbers $p$ for which $8 p+1$ is: a) a perfect square? b) a perfect cube

Your answer

Official solution

Answer. a) $p=3 ;$ b) such $p$ does not exist. Solution. See problem 8.2.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.