Ramanujan Primes and Negative Pell’s Equation

Authors

  • V. Sangeetha Department of Mathematics National College(Autonomous) (Affiliated to Bharathidasan University), Trichy - 620001,Tamil Nadu, India.
  • T. Anupreethi * PG and Research Department of Mathematics.
  • S. Manju Somanath Department of Mathematics, National College(Autonomous)( Affiliated to Bharathidasan University), Trichy - 620 001, Tamil Nadu, India.

https://doi.org/10.22105/opt.v2i4.92

Abstract

The Diophantine equation under consideration to find the non-zero integral solution are of the type x2 = (Rp)y2 − (R1)t which represents a very general type of negative Pell’s equation formed using Ramanujan primes as coefficients. The equation are all formed using the first 10 Ramanujan primes 2,11,17,29,41,47,59,67,71 & 97. Fixing the 1st Ramanujan prime R1 = 2, we seek for solutions of Pell’s equation with coefficients Rp, where Rp denotes the pth Ramanujan prime. MSC Classification Number : 11D09,11D99.

Keywords:

Diophantine equation, Ramanujan prime, Negative pell’s equation, Integral solutions, Brah-magupta lemma

References

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Published

2025-09-30

Issue

Vol. 2 No. 4 (2025): OPT

Section

Articles

How to Cite

Sangeetha, V., Anupreethi, T., & Somanath, S. M. (2025). Ramanujan Primes and Negative Pell’s Equation. Optimality, 2(4), 271-279. https://doi.org/10.22105/opt.v2i4.92