Thread: Problem 29
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Old July 1st, 2007, 09:41 PM
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Quote:
Originally Posted by ThePerfectHacker View Post
2)Let a_1,a_2,...,a_n be distinct integers from \{1,2,...,n\} not necessarily in that order. Show that if n is odd then (a_1-1)(a_2-1)...(a_n-1) is an even number.
As a_1,a_2,...,a_n are distinct integers from \{1,2,...,n\} they are infact a permutation of \{1,2,...,n\}, so one of the a_i's is 1.

Hence one of the terms (a_i-1) is zero so the product is zero, and so even irrespective of the parity of n.

Or have I misread the question.

RonL
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