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ab + bc + ac = (a + b -c)(b + c - a)(c + a - b) for gcd(a,b,c)=1

Source: 2017 Latvia BW TST P14

December 18, 2022
number theoryDiophantine Equationsdiophantine

Problem Statement

Can you find three natural numbers a,b,ca, b, c whose greatest common divisor is 11 and which satisfy the equality ab+bc+ac=(a+b−c)(b+c−a)(c+a−b)?ab + bc + ac = (a + b -c)(b + c - a)(c + a - b) ?
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