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Relatively terms of a Geometric Series

Source: Tournament of Towns Fall 2015 Senior A-level

February 23, 2017

number theoryalgebrageometric sequencegeometric series

Problem Statement

A geometrical progression consists of

37

positive integers. The first and the last terms are relatively prime numbers. Prove that the

19^{th}

term of the progression is the

18^{th}

power of some positive integer. (

3

points)