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USAMO 1983 Problem 5 - Open interval of length 1/n

Source: USAMO 1983 Problem 5

August 16, 2011
AMCUSA(J)MOUSAMOnumber theory unsolvednumber theory

Problem Statement

Consider an open interval of length 1/n1/n on the real number line, where nn is a positive integer. Prove that the number of irreducible fractions p/qp/q, with 1≤q≤n1\le q\le n, contained in the given interval is at most (n+1)/2(n+1)/2.
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