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2021 AMC Fall 10BProblem 12P11-15~4 minPrint
Algebraic ManipulationNumber PropertiesApply an identity: SFFT, sum of squares, difference of cubes, VietaTest small/specific values or special cases to find or verify the answer

Which of the following conditions is sufficient to guarantee that integers xx , yy , and zz satisfy the equation x(x−y)+y(y−z)+z(z−x)=1?x(x-y)+y(y-z)+z(z-x) = 1?

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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.