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Find all prime triples

Source: Turkey Junior National Olympiad 2013 P2

November 29, 2013
modular arithmeticnumber theory proposednumber theory

Problem Statement

Find all prime numbers p,q,rp, q, r satisfying the equation p4+2p+q4+q2=r2+4q3+1 p^4+2p+q^4+q^2=r^2+4q^3+1
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