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2024 AMC 10AProblem 23P21-25~6 minPrint
Systems of EquationsDiophantine EquationsApply an identity: SFFT, sum of squares, difference of cubes, VietaSplit into exhaustive cases and handle each

Integers aa , bb , and cc satisfy ab+c=100ab + c = 100 , bc+a=87bc + a = 87 , and ca+b=60ca + b = 60 . What is ab+bc+ca?ab + bc + ca?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.