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Tuymaada 2017 P1 Day1 Senior League

Source:

July 25, 2017
functionalgebra

Problem Statement

Functions ff and gg are defined on the set of all integers in the interval [−100;100][-100; 100] and take integral values. Prove that for some integral kk the number of solutions of the equation f(x)−g(y)=kf(x)-g(y)=k is odd.\\ ( A. Golovanov)
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