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Natural numbers in Harmonic Progression

Source: CIIM 2015, India Postal Coaching 2015

December 2, 2015

number theorybounded

Problem Statement

Prove that there exists a real number

C > 1

with the following property. Whenever

n > 1

and

a_0 < a_1 < a_2 <\cdots < a_n

are positive integers such that

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

form an arithmetic progression, then

a_0 > C^n

.

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