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Diophantine equation in primes

Source: Dürer Competition Finals 2023/E+ 2

March 8, 2023
number theoryDiophantine equation

Problem Statement

a) Find all solutions of the equation p2+q2+r2=pqrp^2+q^2+r^2=pqr, where p,q,rp,q,r are positive primes.\\ b) Show that for every positive integer NN, there exist three integers a,b,c≥Na,b,c\geq N with a2+b2+c2=abca^2+b^2+c^2=abc.
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