Hello,

denote all these numbers , , ... , with the property :

Now note that when , we have , and it follows that :

This is not a proof in itself : it is there to help you grasp what this problem means. All you have to prove is that there is no solution for where .

Here is an idea : say . Therefore, the following holds : , and so on following the same logic with , , .... Take the squares of these inequalities, and see where you get You will very likely stumble upon a difficulty, that you will probably be able to express in mathematical terms and that will lead to the solution to your problem