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2009 IMO Problems/Problem 1

Revision as of 05:08, 23 July 2009 by Bugi (talk | contribs) (Created page with '== Problem == Let <math>n</math> be a positive integer and let <math>a_1,\ldots,a_k (k\ge2)</math> be distinct integers in the set <math>\{1,\ldots,n\}</math> such that <math>n…')
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Problem

Let $n$ be a positive integer and let $a_1,\ldots,a_k (k\ge2)$ be distinct integers in the set $\{1,\ldots,n\}$ such that $n$ divides $a_i(a_{i+1}-1)$ for $i=1,\ldots,k-1$. Prove that $n$ doesn't divide $a_k(a_1-1)$.

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