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Part of 1988 India National Olympiad

Problems(1)

Indian Mathematical Olympiad 1988 - Problem 1

Source:

m_1,m_2,m_3,\dots,m_n

be a rearrangement of the numbers

1,2,\dots,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.

number theory proposednumber theory