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<p>During the mid-winter recess, <strong>Milan Haiman</strong> participated as a member of the <strong>Hungarian Math Olympic Team</strong> in the <strong>Romanian Master of Mathematics</strong> (RMM), an <strong>International Math Olympiad</strong>.</p>
<p>Milan received a <strong>silver medal</strong> for his performance, <strong>finishing 27th place internationally</strong> and <strong>receiving the high score on the Hungarian Team</strong>. Congratulations on this accomplishment, Milan!</p>
<p>Here is one of the problems on which Milan's solution received a perfect score:</p>
<p>Given any positive real number ε, prove that, for all but finitely many positive integers v, any graph on v vertices with at least (1 + ε)v edges has two distinct simple cycles of equal lengths. (Recall that the notion of a simple cycle does not allow repetition of vertices in a cycle.) [RMM Problem #3]</p>
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