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IMO LongList 1967, Sweden 2

Source: IMO LongList 1967, Sweden 2

December 16, 2004
trigonometryInequalityTrigonometric inequalityminimumIMO ShortlistIMO Longlist

Problem Statement

Let nn and kk be positive integers such that 1≤n≤N+11 \leq n \leq N+1, 1≤k≤N+11 \leq k \leq N+1. Show that: min⁡n≠k∣sin⁡n−sin⁡k∣<2N. \min_{n \neq k} |\sin n - \sin k| < \frac{2}{N}.
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