Volume 32, 2026, Number 2 (Online First)

Volume 32 ▶ Number 1 ▷ Number 2 (Online First)

  • Volume opened: 1 April 2026
  • Status: In progress

On the inverse of a certain triangular matrix and its connection to the largest odd divisor
Original research paper. Pages 255–262
Sela Fried
Full paper (PDF, 196 Kb) | Abstract

The inverse R of a certain infinite triangular matrix A is shown to be directly related to the largest odd divisor function, thus proving a conjecture of Barry. We also provide a proof of a formula for R given by Yin and obtain bivariate generating functions for A and R.

A note on Leibniz rule for difference quotient
Original research paper. Pages 263–268
Taekyun Kim and Dae San Kim
Full paper (PDF, 161 Kb) | Abstract

In this note, we derive a Leibniz rule for difference quotient.

Simpler congruences for Jacobi sum J(1,1)49 of order 49
Original research paper. Pages 269–280
Ishrat Jahan Ansari, Vikas Jadhav and Devendra Shirolkar
Full paper (PDF, 237 Kb) | Abstract

Congruences of order l^2 (with l an odd prime) were obtained by D. Shirolkar and S. A. Katre [15]. In this paper we determine congruence of Jacobi sums J(1,1)_{49} of order 49 over a field {\mathbb F}_{p}. We also show that simpler congruences hold for J(1,1)_{49} in the case of artiad and hyperartiad primes.

q-Leonardo polynomials
Original research paper. Pages 281–299
Naim Tuglu, Sude Sıla Ekinci and Miraç Çetin Keskin
Full paper (PDF, 327 Kb) | Abstract

In this study, we define the q-Leonardo Pisano polynomials and q-Leonardo Lucas polynomials of the first and the second kinds, collectively termed q-Leonardo polynomials. We investigate some interesting properties of the new polynomials.

Generalizing Pascal’s row sums to complex orders: A Poisson summation approach
Original research paper. Pages 300–312
Fabrizio Mancini
Full paper (PDF, 808 Kb) | Abstract

We generalize Pascal’s triangle row sums by defining shifted fractional binomial coefficients with a real scaling parameter and a complex shift. Using the Poisson summation formula, we derive exact summation identities extended via analytic continuation to conditionally convergent regimes. We prove that when the magnitude of the scaling parameter is not greater than 2, the sum collapses to a simple exponential form independent of the shift; otherwise, it generalizes classical series multisections to non-integer steps and complex shifts. These closed forms allow for rapid and exact computation even where symbolic algebra systems fail.

This volume of the International Journal “Notes on Number Theory and Discrete Mathematics” is published with the financial support of the Bulgarian National Science Fund, Grant Ref. No. KP-06-NP7/2/03.12.2025. Bulgarian National Science Fund bears no liability for the content of the published materials.

Volume 32 ▶ Number 1 ▷ Number 2 (Online First)

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