2018/07/05 by Nikola Adžaga, Adžaga, Nikola
Mathematics · #11D09 #11J68 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1807.01896
openalex publication_date 2018/07/05 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
A Diophantine m-tuple is a set of m distinct integers such that the\nproduct of any two distinct elements plus one is a perfect square. It was\nrecently proven that there is no Diophantine quintuple in positive integers. We\nstudy the same problem in the rings of integers of imaginary quadratic fields.\nBy using a gap principle proven by Diophantine approximations, we show that\nm leqslant 42. Our proof is relatively simple compared to the proofs of the\nsimilar results in positive integers.\n