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O 12

Source:

May 25, 2007
inductionmodular arithmetic

Problem Statement

Let mm and nn be positive integers. If x1x_1, x2x_2, ⋯\cdots, xmx_m are positive integers whose arithmetic mean is less than n+1n+1 and if y1y_1, y2y_2, ⋯\cdots, yny_n are positive integers whose arithmetic mean is less than m+1m+1, prove that some sum of one or more xx's equals some sum of one or more yy's.
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