Open AccessThe Quadratic Diophantine Equations x^2− P(t)y^2− 2P′(t)x + 4P(t)y + (P′(t))^2− 4P(t) − 1 = 0
Author(s) -
Amara Chandoul,
Diego Marques,
Samira Shaban Albrbar
Publication year - 2019
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v11n2p30
Subject(s) - mathematics , diophantine equation , integer (computer science) , prime (order theory) , combinatorics , quadratic equation , square (algebra) , discrete mathematics , geometry , computer science , programming language
Let P := P(t) be a non square polynomial. In this paper, we consider the number of integer solutions of Diophantine equation
E : x2− P(t)y2− 2P′(t)x + 4P(t)y + (P′(t))2− 4P(t) − 1 = 0.
We derive some recurrence relations on the integer solutions (xn,yn) of E. In the last section, we consider the same problem over finite fields Fpfor primes p ≥ 5. Our main results are generaliations of previous results given by Ozcok and Tekcan (Ozkoc and Tekcan, 2010).