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for odd prime p, p^2(p^2 -1999) is divisible by 6 but not by 12

Source: 1999 Estonia National Olympiad Final Round grade 9 p1

March 13, 2020
divisibleprimesoddnumber theory

Problem Statement

Prove that if pp is an odd prime, then p2(p2āˆ’1999)p^2(p^2 -1999) is divisible by 66 but not by 1212.
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