IMO-2009-1

Discussion on International Mathematical Olympiad (IMO)
Tahmid Hasan
Posts: 665
Joined: Thu Dec 09, 2010 5:34 pm

IMO-2009-1

Let $n$ be a positive integer and let $a_1, . . . , a_k (k \geq 2)$ be distinct integers in the set ${{{1, . . . ,n}}}$ such that $n$ divides $a_i(a_{i+1} −1)$ for $i = 1, . . . ,k−1$. Prove that $n$ does not divide $a_k(a_1−1)$.
[easiest IMO (contest) problem of 21st century................to me ]
বড় ভালবাসি তোমায়,মা

*Mahi*
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Re: IMO-2009-1

If anybody need a hint...
Use $L^AT_EX$, It makes our work a lot easier!