D. I. Khomovsky

activity

20152026

most citedEfficient computation of terms of linear recurrence sequences of any order

3 citations · 4 across the 8 of their papers we have counts for

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6 papers · 1 filter

math.NT2026

Congruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution Sets

Max A. Alekseyev, Dmitry I. Khomovsky

Let $A$ and $B$ be polynomials with integer coefficients. We study nonzero integer solutions of $y ∣ A (x), x ∣ B (y),$ using quotient transformations that may change the…

math.NT2020

On natural densities of sets of some type integers

Dmitry I. Khomovsky

Let $a_{0} = b_{0} = 0$ and $0 < a_{1} \leq b_{1} < a_{2} \leq b_{2} < \dots \leq b_{n}$ be integers. Let $Q (x; ⋃_{j = 1}^{n} [a_{j}, b_{j}])$ be the number of integers between $1$ and $x$ such th…

math.NT2018

A geometric approach to integer factorization

Dmitry I. Khomovsky

We give a geometric approach to integer factorization. This approach is based on special approximations of segments of the curve that is represented by $y = n / x$ , where $n$ is the in…

math.NT2016★ 3 cited

Efficient computation of terms of linear recurrence sequences of any order

Dmitry I. Khomovsky

In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indi…

math.NT2016

A method for obtaining Fibonacci identities

Dmitry I. Khomovsky

For the Lucas sequence ${U_{k} (P, Q)}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrenc…

math.NT2015★ 1 cited

On the relationship between the number of solutions of congruence systems and the resultant of two polynomials

Dmitry I. Khomovsky

Let $q$ be an odd prime and $f (x)$ , $g (x)$ be polynomials with integer coefficients. If the system of congruences $f (x) \equiv g (x) \equiv 0 (mod q)$ has $ℓ$ solutions, then $R…