TY - JOUR
TI - The Solution of Fermatâ€™s Two Squares Equation and Its Generalization In Lucas Sequences
PY - 2024/06/01
Y2 - 2024/09/20
JF - Baghdad Science Journal
JA - Baghdad Sci.J
VL - 21
IS - 6
SE - article
DO - 10.21123/bsj.2023.8786
UR - https://doi.org/10.21123/bsj.2023.8786
SP - 2079
AB - As it is well known, there are an infinite number of primes in special forms such as Fermat's two squares form, p=x^2+y^2 or its generalization, p=x^2+y^4, where the unknowns x, y, and p represent integers. The main goal of this paper is to see if these forms still have an infinite number of solutions when the unknowns are derived from sequences with an infinite number of prime numbers in their terms. This paper focuses on the solutions to these forms where the unknowns represent terms in certain binary linear recurrence sequences known as the Lucas sequences of the first and second types.
ER -