
TL;DR
This paper classifies all integer triples (a, b, n) where no large Zsigmondy prime exists, extending understanding of prime divisors in exponential differences and their properties.
Contribution
It provides a complete classification of triples (a, b, n) lacking large Zsigmondy primes, a novel result in the study of prime divisors of exponential expressions.
Findings
Identifies all (a, b, n) with no large Zsigmondy prime
Characterizes conditions under which large Zsigmondy primes do not exist
Enhances understanding of prime divisors in exponential differences
Abstract
If and are positive integers and and are relatively prime integers, then a large Zsigmondy prime for is a prime such that but for and either or . We classify all the triples of integers for which no large Zsigmondy prime exists.
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Taxonomy
TopicsAnalytic Number Theory Research · Historical Studies and Socio-cultural Analysis · History and Theory of Mathematics
