WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Note on the Transcendental Equation with Three Unknowns √2f(z) − 4 = √x − P′(t) + √P(t)(y + 2) ± √ x − P′(t) − √ P(t)(y + 2)
Author:
Abstract: Let $$P := P(t) $$ be a non square polynomial and $$f := f(z)$$ be a bijective application over $$Z$$. Using the method of continuous fractions, we consider, in this paper, the number of integer solutions of transcendental equation
$$\sqrt {2f(z) − 4 }= \sqrt {x − P′(t) + \sqrt {P(t)(y + 2)}} ± \sqrt { x − P′(t) − \sqrt { P(t)(y + 2)}}$$.
under the condition that
$$ x^{2} − P(t)y^{2} − 2P^{′}(t)x + 4P(t)y + (P^{′}(t))^{2} − 4P(t) − 1 = 0$$. We extend a previous result given by A. S. Sriram and P. Veeramallan