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Find the maximum value of f(n) - ILL 1990 IND2

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September 18, 2010
functionfloor functionalgebra proposedalgebra

Problem Statement

Function f(n),n∈Nf(n), n \in \mathbb N, is defined as follows: Let (2n)!n!(n+1000)!=A(n)B(n)\frac{(2n)!}{n!(n+1000)!} = \frac{A(n)}{B(n)} , where A(n),B(n)A(n), B(n) are coprime positive integers; if B(n)=1B(n) = 1, then f(n)=1f(n) = 1; if B(n)≠1B(n) \neq 1, then f(n)f(n) is the largest prime factor of B(n)B(n). Prove that the values of f(n)f(n) are finite, and find the maximum value of f(n).f(n).
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