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Factoring 2024 in Z[\sqrt{3}]

Source: Czech-Polish-Slovak Junior Match 2024, T-2

May 29, 2024
number theorynumber theory proposedalgebraalgebra proposed

Problem Statement

Among all triples (a,b,c)(a,b,c) of natural numbers satisfying (a+143)(b14c3)=2024,(a+14\sqrt{3})(b-14c\sqrt{3})=2024, determine the one with the maximal value of aa.