# Difference between revisions of "2011 IMO Problems/Problem 5"

Humzaiqbal (talk | contribs) (Created page with "Let f be a function from the set of integers to the set of positive integers. Suppose that, for any two integers m and n, the difference f (m) − f (n) is divisible by f (m − ...") |
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− | Let f be a function from the set of integers to the set of positive integers. Suppose that, for any two integers m and n, the difference f (m) | + | Let <math>f</math> be a function from the set of integers to the set of positive integers. Suppose that, for any two integers <math>m</math> and <math>n</math>, the difference <math>f(m) - f(n)</math> is divisible by <math>f(m - n)</math>. Prove that, for all integers <math>m</math> and <math>n</math> with <math>f(m) \leq f(n)</math>, the number <math>f(n)</math> is divisible by <math>f(m)</math>. |

## Revision as of 13:41, 27 November 2011

Let be a function from the set of integers to the set of positive integers. Suppose that, for any two integers and , the difference is divisible by . Prove that, for all integers and with , the number is divisible by .