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Part of 2016 Czech-Polish-Slovak Junior Match

Problems(1)

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

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

1/20/2020
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.
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Diophantine equationsystem of equationsDiophantine Equationsdiophantinenumber theory