# Let P={4,8,9,16,25,cdots,} be the set of perfect powers, i.e., the set of positive integers of the form a^b, where a,b are integers greater than 1. Prove that sum_(j in P) 1/(j-1) = 1?

Then teach the underlying concepts
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#### Explanation

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#### Explanation:

I want someone to double check my answer

1
Nimo N. Share
Feb 24, 2018

See below.

#### Explanation:

"According to Euler, Goldbach showed (in a now lost letter) that the sum of  1/p − 1  over the set of perfect powers p, excluding 1 and excluding duplicates, is 1."

"This is sometimes known as the Goldbach-Euler theorem."

Quotes are from article discussing perfect powers at:
https://en.wikipedia.org/wiki/Perfect_power#Examples_and_sums

As for doing the proof, I abstain from attempting it.

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