## Prime Reciprocals

#### Problem

Given that P = {`p`_{1}, `p`_{2}, ... , `p`_{k}} is a set of distinct, not necessarily consecutive primes, prove that 1/`p`_{1} + 1/`p`_{2} + ... 1/`p`_{k} is never integer.

Problem ID: 238 (02 Aug 2005) Difficulty: 4 Star