3 papers
math.NT2026
Computing bounded solutions to linear Diophantine equations with the sum of divisors
Max A. Alekseyev
We propose an efficient computational method for finding all solutions to the Diophantine equation , where integer coefficient and an upper bound…
math.QA2025
Classifying integral Grothendieck rings up to rank 5 and beyond
Max A. Alekseyev, Winfried Bruns, Jingcheng Dong +1
In this paper, we define a Grothendieck ring as a fusion ring categorifiable into a fusion category over the complex field. An integral fusion ring is called Drinfeld if all its fo…
math.NT2025
On the -adic valuations of values of Legendre polynomials
Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also…