## 14S. Different Approaches to an Intuitive Problem

December 8, 2008 by Ofir Gorodetsky

The fourth problem of the second season of PEN is as follows:

N17. Suppose that and are distinct real numbers such that:

are all integers. Show that and are integers.

Here is the official solution file: pen14.pdf

You can discuss the problem in MathLinks here.

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on December 14, 2008 at 3:43 pm |AnonymousHave some problem related to this problem . For example :

1) Condition n can replace by prime p .

2) a,b is two rational and condition occurs for infinite natural n .