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BMO Round 1, 2015

Number theory Difficulty 6.0 National Olympiad Prove it United Kingdom

Determine all functions f(n)f(n) from the positive integers to the positive integers which satisfy the following condition: whenever aa, bb and cc are positive integers such that 1/a+1/b=1/c1/a + 1/b = 1/c, then
1/f(a)+1/f(b)=1/f(c).1/f(a) + 1/f(b) = 1/f(c).

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