Ramanujan Primes and Negative Pell’s Equation - Sangeetha, V.; Anupreethi, T.; Somanath, S. Manju (Optimality, 2025)
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.