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Exist p,m for every n(CGMO 2010-P3)

Source:

August 17, 2010
modular arithmeticnumber theoryrelatively primenumber theory proposed

Problem Statement

Prove that for every given positive integer nn, there exists a prime pp and an integer mm such that (a)(a) p≡5(mod6)p \equiv 5 \pmod 6 (b)(b) p∤np \nmid n (c)(c) n≡m3(modp)n \equiv m^3 \pmod p
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