1978 IMO Problems/Problem 5
Let be an injective function from in itself. Prove that for any we have:
We know that all the unknowns are integers, so the smallest one must greater or equal to 1.
Let me denote the permutations of with .
From the rearrangement's inequality we know that .
We will denote we permutations of in this form .
So we have .
Let's denote and .
We have . Which comes from .
So we are done.
The above solution was posted and copyrighted by Davron. The original thread for this problem can be found here: 
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