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n > \sqrt{p}-1 when p | (n^6 -1)

Source: 2014 Saudi Arabia Pre-TST 4.1

September 13, 2020
number theoryinequalitiesdividesdivisible

Problem Statement

Let pp be a prime number and n≥2n \ge 2 a positive integer, such that p∣(n6−1)p | (n^6 -1). Prove that n>p−1n > \sqrt{p}-1.
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