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