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2013 China Second Round Olympiad (C) Test 2 Q1

Source: 13 Oct 2013

October 16, 2013
modular arithmeticnumber theory proposednumber theoryParity

Problem Statement

Let nn be a positive odd integer , a1,a2,⋯ ,ana_1,a_2,\cdots,a_n be any permutation of the positive integers 1,2,⋯ ,n1,2,\cdots,n . Prove that :(a1−1)(a22−2)(a33−3)⋯(ann−n)(a_1-1)(a^2_2-2)(a^3_3-3)\cdots (a^n_n-n) is an even number.
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