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Algebra Difficulty 5.1 AIME, harder Prove it Ukraine
Find all integer n, that satisfy the following equality:
(n−1)(n−3)(n−5)…(n−2011)=n(n+2)(n+4)…(n+2010).
Solution
If n is even, then LHS is odd, and RHS is even, and vice versa (for odd n).
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