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On the prime factors of the number 2p-1 - 1

Published online by Cambridge University Press:  18 May 2009

A. Rotkiewicz
A. Rotkiewicz
Affiliation:
Department of Pure MathematicsCambridge University
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From the proof of Theorem 2 of [5] it follows that for every positive integer k there exist infinitely many primes p in the arithmetical progression ax + b (x = 0, 1, 2,…), where a and b are relatively prime positive integers, such that the number 2p−1 − 1 has at least k composite factors of the form (p − 1)x + 1. The following question arises:

For any given natural number k, do there exist infinitely many primes p such that the number 2p−1 − 1 has k prime factors of the form(p − 1)x + 1 and p ≡ b (mod a), where a and b are coprime positive integers?

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 2 , July 1968 , pp. 83 - 86
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

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