1978 IMO Problems/Problem 5
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Problem
Let be an injective function from
in itself. Prove that for any
we have:
Solution
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: [1]
See Also
1978 IMO (Problems) • Resources | ||
Preceded by [[1978 IMO Problems/Problem {{{num-b}}}|Problem {{{num-b}}}]] |
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