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Show that there exist..

Source: Indian RMO 1996 Problem 6

October 26, 2005

Problem Statement

Given any positive integer nn , show that there are two positive rational numbers aa and bb , a≠ba \not= b, which are not integers and which are such that a−b,a2−b2,…an−bna - b, a^2 - b^2 , \ldots a^n - b^n are all integers.
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