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prove that 4p-3 is a square

Source: India tst 2003, p10

March 13, 2012
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let nn be a positive integer greater than 11, and let pp be a prime such that nn divides p−1p-1 and pp divides n3−1n^3-1. Prove that 4p−34p-3 is a square.
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