Amara Chandoul, "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)," WSEAS Transactions on Mathematics, vol. 21, pp. 356-360, 2022, DOI:10.37394/23206.2022.21.42
Amara Chandoul. 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).
WSEAS Transactions on Mathematics. 2022;21:356-360. 10.37394/23206.2022.21.42
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 <br><br>
$$\sqrt {2f(z) − 4 }= \sqrt {x − P′(t) + \sqrt {P(t)(y + 2)}} ± \sqrt { x − P′(t) − \sqrt { P(t)(y + 2)}}$$. <br>
under the condition that<br>
$$ x^{2} − P(t)y^{2} − 2P^{′}(t)x + 4P(t)y + (P^{′}(t))^{2} − 4P(t) − 1 = 0$$. We extend a previous result given by A. S. Sriram and P. Veeramallan
Keywords:
Transcendental equation, Integer solutions, Diophantine Equation, Pell equation, Polynomial, Bijection, Continued fraction, Recurrence relation
Pages: 356-360 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 21, 2022, Art. #42 DOI: 10.37394/23206.2022.21.42
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