Exponential Diophantine Equations Concerning Numbers in Reverse Order | Chapter 9 | Research Updates in Mathematics and Computer Science Vol. 7

 

In this scholarly article, we delve into the intricate realm of exponential Diophantine equations, specifically those pertaining to the reversal of digits denoted by 29𝑥 +92𝑦 =𝑧2, 38𝑥 +83𝑦 =𝑧2, 47𝑥 +74𝑦 =𝑧2, 56𝑥 +65𝑦 =𝑧2. Within this context, to determine if a distinct solution exists for the considered exponential equation, it is finally revealed that it has infinitely many solutions, but all of the aforesaid exponential equations have a similar solution, identified as (1,1,11).

 

 

Author(s) Details

Janaki G.

Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy – 18, India.

Gowri Shankari A.

Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy – 18, India.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v7/437

 

Exponential Diophantine Equations Concerning Numbers in Reverse Order | Chapter 10 | Research Updates in Mathematics and Computer Science Vol. 7

 

In this scholarly article, we delve into the intricate realm of exponential Diophantine equations, specifically those pertaining to the reversal of digits denoted by 29x    Within this context, to determine if a distinct solution exists for the considered exponential equation, it is finally revealed that it has infinitely many solutions, but all of the aforesaid exponential equations have a similar solution, identified as (1, 1, 11).

 

Author(s)details:-

 

Janaki G. (Associate Professor)
Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy – 18, India.

 

Gowri Shankari A. (Assistant Professor)
Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Trichy – 18, India.

 

Please See the book here :- https://doi.org/10.9734/bpi/rumcs/v7/437

Biquadratic Equation with Four Unknowns | Chapter 11 | Novel Research Aspects in Mathematical and Computer Science Vol. 3

 Number theory is strongly reliant on diophantine equations, which can take many different forms. There are a variety of Diophantine equations that have no solution, trivial solutions, a finite number of solutions, and an infinite number of solutions. There are essentially two types of equations among higher degree Diophantine Equations. They are homogeneous and non-homogeneous bi-quadratic equations when the degree is four. Its integral solution may be required in its most basic form. Many mathematicians have been fascinated by both homogeneous and non-homogeneous Biquadratic equations since ancient times. The challenge of identifying non-trivial integral solutions of the non-homogeneous Biquadratic equation with four unknowns provided by 7xy + 3z2 = 3 w4 is addressed in this study. The linear transformations x = u + v, y = u - v, and z = v are used to find an infinite number of non-zero integer solutions to the equation.

 

 

Author(S) Details

Shreemathi Adiga
Department of Mathematics, Government First Grade College, Koteshwara, Kundapura Taluk, Udupi – 57622, Karnataka, India.

View Book:- https://stm.bookpi.org/NRAMCS-V3/article/view/6818