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diophantine systema, a + b = c , a^2 + b^3 = c^2

Source: 2022 Czech-Polish-Slovak Match Junior, team p4 CPSJ

September 3, 2022

number theoryDiophantine equationDiophantine Equationsdiophantine

Problem Statement

Find all triples

(a, b, c)

of integers that satisfy the equations

a + b = c

and

a^2 + b^3 = c^2