Simpler congruences for Jacobi sum J(1,1)49 of order 49

Ishrat Jahan Ansari, Vikas Jadhav and Devendra Shirolkar
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 2, Pages 269–280
DOI: 10.7546/nntdm.2026.32.2.269-280
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Authors and affiliations

Ishrat Jahan Ansari
Department of Mathematics, M.C.E. Society’s Abeda Inamdar Senior College, Savitribai Phule Pune University
Research Scholar, Sir Parshurambhau College
Pune, Maharashtra, India

Vikas Jadhav
Department of Mathematics, Nowrosjee Wadia College
Pune, Maharashtra, India

Devendra Shirolkar
Savitribai Phule Pune University
Pune, Maharashtra, India

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.

Keywords

  • Jacobi sums
  • Cyclotomic numbers
  • Congruences
  • Dickson–Hurwitz sums

2020 Mathematics Subject Classification

  • 11T22
  • 11T24

References

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Manuscript history

  • Received: 9 May 2025
  • Revised: 3 March 2026
  • Accepted: 16 April 2026
  • Online First: 24 April 2026

Copyright information

Ⓒ 2026 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Ansari, I. J., Jadhav, V., & Shirolkar, D. (2026). Simpler congruences for Jacobi sum J(1,1)49 of order 49. Notes on Number Theory and Discrete Mathematics, 32(2), 269-280, DOI: 10.7546/nntdm.2026.32.2.269-280.

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