A generalized Ramanujan-Nagell equation related to certain strongly regular graphs

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Abstract

A quadratic-exponential Diophantine equation in 4 variables, describing certain strongly regular graphs, is completely solved. Along the way we encounter different types of generalized Ramanujan-Nagell equations whose complete solution can be found in the literature, and we come across a problem on the order of the prime ideal above 2 in the class groups of certain imaginary quadratic number fields, which is related to the size of the squarefree part of 2^n - 1 and to Wieferich primes, and the solution of which can be based on the abc-conjecture.
Original languageEnglish
Pages (from-to)A35/1-13
Number of pages13
JournalIntegers : Electronic Journal of Combinatorial Number Theory
Volume14
Publication statusPublished - 2014

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