# 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
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### 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.

• 13 minutes ago
• 23 minutes ago
• 27 minutes ago
• 35 minutes ago
• 59 seconds ago
• 4 minutes ago
• 8 minutes ago
• 8 minutes ago
• 11 minutes ago
• 12 minutes ago
• 13 minutes ago
• 23 minutes ago
• 27 minutes ago
• 35 minutes ago