REA Press Null REA Press3042-01993042-0199 REA Press https://doi.org/10.22105/opt.v2i4.92 Research Article Diophantine equation, Ramanujan prime, Negative pell’s equation, Integral solutions, Brah-magupta lemma. Ramanujan Primes and Negative Pell’s EquationRamanujan Primes and Negative Pell’s Equation Sangeetha V. Department of Mathematics National College(Autonomous) (Affiliated to Bharathidasan University), Trichy - 620001,Tamil Nadu, India. Anupreethi T. PG and Research Department of Mathematics. Somanath S. Manju Department of Mathematics, National College(Autonomous)( Affiliated to Bharathidasan University), Trichy - 620 001, Tamil Nadu, India. 10 2025 05 10 2025 2 4 © 2025 REA Press 2025

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 Ramanujan Primes and Negative Pell’s Equation

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.

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