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diophantine system parameter, a + b + c = 3k + 1, ab + bc + ca = 3k^2 + 2k

Source: Czech-Polish-Slovak Junior Match 2016, team p6 CPSJ

January 20, 2020
Diophantine equationsystem of equationsDiophantine Equationsdiophantinenumber theory

Problem Statement

Let kk be a given positive integer. Find all triples of positive integers a,b,ca, b, c, such that a+b+c=3k+1a + b + c = 3k + 1, ab+bc+ca=3k2+2kab + bc + ca = 3k^2 + 2k.
Slovakia
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