Difference of powers of consecutive primes which are perfect squares

2016/04/18 by Alessandro Ventullo, Ventullo, Alessandro
Mathematics · #11AXX #11DXX #Advanced Mathematical Theories #Analytic Number Theory Research #Arithmetic #Combinatorics #Discrete mathematics #FOS: Mathematics #Geometry #Mathematics #Mathematics and Applications #Natural number #Number Theory (math.NT) #Square (algebra) #math.NT #msc:11AXX #msc:11DXX

paper · pdf · doi:10.48550/arxiv.1604.05334

published in arXiv (Cornell University) (Cornell University)

arxiv created 2016/04/18 · openalex publication_date 2016/04/18 · arxiv updated 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the consecutive primes p and q (p > q) for which there exists a pair of natural numbers (x,y) such that p^x-q^y is a perfect square and make some conjectures.

Citations

• Primary cyclotomic units and a proof of Catalans conjecture

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