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problem 5 of Indian Mathematical Olympiad 1989

Source: Number theory (divisibility)

September 1, 2009
number theory unsolvednumber theory

Problem Statement

For positive integers n n, define A(n) A(n) to be (2n)!(n!)2 \frac {(2n)!}{(n!)^{2}}. Determine the sets of positive integers n n for which (a) A(n) A(n) is an even number, (b) A(n) A(n) is a multiple of 4 4.
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