IMO 2009 (very easy number theory, huh?)
. Let n be a positive integer and let a1, . . . , ak (k ≥ 2) be distinct
integers in the set{1, . . . , n} such that n divides ai(ai+1−1) for i = 1,
. . . , k−1. Prove that n does not divide ak( a1−1 ).
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