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## 14S. Different Approaches to an Intuitive Problem

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

N17. Suppose that $a$ and $b$ are distinct real numbers such that:
$a - b, a^{2}-b^{2}, \cdots, a^k-b^k, \cdots$ are all integers. Show that $a$ and $b$ are integers.

Here is the official solution file: pen14.pdf

You can discuss the problem in MathLinks here.