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CIIM 2015 Problem 6

Source:

August 9, 2016

CIIM 2015undergraduatearithmetic sequence

Problem Statement

Show that there exists a real

C > 1

that satisfy the following property: if

n > 1

and

a_0 < a_1 < \cdots < a_n

are positive integers such that

\frac{1}{a_0},\frac{1}{a_1},\dots,\frac{1}{a_n}

are in arithmetic progression, then

a_0 > C^n.

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