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Source: EMC 2023 Juniors P1

December 18, 2023
nt2023emcnumber theoryGCD

Problem Statement

Suppose a,b,ca,b,c are positive integers such that gcd⁡(a,b)+gcd⁡(a,c)+gcd⁡(b,c)=b+c+2023\gcd(a,b)+\gcd(a,c)+\gcd(b,c)=b+c+2023 Prove that gcd⁡(b,c)=2023\gcd(b,c)=2023.
Remark. For positive integers xx and yy, gcd⁡(x,y)\gcd(x,y) denotes their greatest common divisor.
Ivan Novak
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