# Solution September 11, 2007

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### Solution

Assume for the sake of contradiction that we have *a* and *b* such that and

Then

With this gives

Let

can not be so we have .
Choose and among the solutions of **(1)** such that and is minimal.

Then, on the one hand,

where . Since , the second term is positive, and

On the other hand, if is a solution of **(1)** then so is . By the minimality condition, we have , i.e.

This is a contradiction to the previous inequality, completing the proof.