N. Krylov

activity

20002020

most citedZeta(n) via hyperbolic functions

26 citations · 29 across the 11 of their papers we have counts for

collaborators

14 papers

math.CA2020

Combinatorial properties of irreducible Laguerre polynomials in two variables

Nikolai A. Krylov

Following our earlier work, where doubly indexed and irreducible over Q two-variable Laguerre polynomials were introduced, we prove for such polynomials some recurrence formulas an…

math.GR2019

Permutations with a distinct divisor property

Mohammad Javaheri, Nikolai A. Krylov

A finite group of order $n$ is said to have the distinct divisor property (DDP) if there exists a permutation $g_{1}, \dots, g_{n}$ of its elements such that $g_i^{-1}g_{i+1} \neq g_j^…

math.NT2018★ 1 cited

Complete Generalized Fibonacci Sequences Modulo Primes

Mohammad Javaheri, Nikolai Krylov

We study generalized Fibonacci sequences $F_{n + 1} = P F_{n} - Q F_{n - 1}$ with initial values $F_{0} = 0$ and $F_{1} = 1$ . Let $P, Q$ be nonzero integers such that $P^{2} - 4 Q$ is not a perfect square.…

math.NT2016

On the subgroup generated by solutions of Pell's equation

Elena C. Covill, Mohammad Javaheri, Nikolai A. Krylov

Equivalence classes of solutions of the Diophantine equation $a^{2} + m b^{2} = c^{2}$ form an infinitely generated abelian group $G_{m}$ , where $m$ is a fixed square-free positive integer. Sol…

math.CA2014

A congruence property of irreducible Laguerre polynomials in two variables

Nikolai A. Krylov, Zhangyuan Li

In this paper we introduce a version of irreducible Laguerre polynomials in two variables and prove for it a congruence property, which is similar to the one obtained by Carlitz fo…

math.NT2014

A basis of the group of primitive almost pythagorean triples

Nikolai A. Krylov

Let $m$ be a fixed square-free positive integer, then equivalence classes of solutions of Diophantine equation $x^{2} + m \cdot y^{2} = z^{2}$ form an infinitely generated abelian group under…