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	The 69th William Lowell Putnam Mathematical Competition Saturday, December 6, 2008 A1 Let f : R2 → R be a function such that f (x, y) + f (y, z) + f (z, x) = 0 for all real numbers x, y, and z. Prove that there exists Add to Reading List Document Date: 2009-03-23 23:24:11 Open Document File Size: 26,12 KB Share Result on Facebook IndustryTerm nontrivial finite / / Position player / / SocialTag Arithmetic Elementary arithmetic Least common multiple Greatest common divisor Euclidean algorithm Greatest common divisor of two polynomials Mathematics Polynomials Multiplicative functions

The 69th William Lowell Putnam Mathematical Competition Saturday, December 6, 2008 A1 Let f : R2 → R be a function such that f (x, y) + f (y, z) + f (z, x) = 0 for all real numbers x, y, and z. Prove that there exists Add to Reading List