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Indian Mathematical Olympiad 1988 - Problem 1

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August 14, 2009
number theory proposednumber theory

Problem Statement

Let m1,m2,m3,…,mn m_1,m_2,m_3,\dots,m_n be a rearrangement of the numbers 1,2,…,n 1,2,\dots,n. Suppose that n n is odd. Prove that the product \left(m_1\minus{}1\right)\left(m_2\minus{}2\right)\cdots \left(m_n\minus{}n\right) is an even integer.
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