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Israel 2015 Q1 - Timely diophantine equation

Source: Israel National Olympiad 2015 Q1

August 7, 2019
Diophantine equationnumber theoryalgebra

Problem Statement

[*] Find an example of three positive integers a,b,ca,b,c satisfying 31a+30b+28c=36531a+30b+28c=365. [*] Prove that any triplet a,b,ca,b,c satisfying the above condition, also satisfies a+b+c=12a+b+c=12.
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