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

Intrinsic Solutions of the Pell Equation x2 = 5y2 + 9t | Chapter 3 | Explorations in Diophantine Equations

 We search for a non-trivial integer solutions to the equation x2= 5y2+ 9t, t ∈ N , where i) t = 2k+1, ii) t = 2k for all k ∈ N , Additionally the recurrence relation for the solutions are also discovered.

Author(s) Details:

S. Vidhya,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

G. Janaki,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

B. Amala,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

Please see the link here: https://stm.bookpi.org/EDE/article/view/12430

On the Ternion Cubical Diophantine Equation 5(m2+n2)-6(mn)+8(m+n)+16=370 p3 | Chapter 2 | Explorations in Diophantine Equations

 The third order Cubic Diophantine equation 5(m + n) -6(mn) + 8(m + n) + 16 = 370p3 is analyzed for infinitely enormous number of non-zero integer solutions.  Also, some fascinating relations among the solutions are exhibited.

Author(s) Details:

P. Saranya,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

G. Janaki,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

K. Poorani,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

Please see the link here: https://stm.bookpi.org/EDE/article/view/12429

An Analysis on the Ternary Quadratic Diophantine Equation r2 + t2 = 10w2 | Chapter 1 | Explorations in Diophantine Equations

 In this work, our main focus is on tracing all the non-zero, infinitely many integral solutions to the ternary quadratic equation r2 + t2 = 10w2. Of these solutions, some dazzling patterns are shown.

Author(s) Details:

G. Janaki,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

S. Shanmuga Priya,
PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

Please see the link here: https://stm.bookpi.org/EDE/article/view/12427

Some Inherent Properties of Pythagorean Triples | Chapter 12 | Research Highlights in Mathematics and Computer Science Vol. 7

 This article revisits the topic of Pythagorean triples with a different perspective. While several methods have been explored to generate Pythagorean triples, none of them is complete in terms of generating all the triples without repetitions. Indeed, many existing methods concentrate on generating primitive triples but do not cater to non-primitives. Also study focused to Geometric Series representation of Set of Pythagorean triples and its relation with above Length of Pythagorean triples.

Author(s) Details:

Thiruchinapalli Srinivas,
Priyadarshini College of Engineering and Technology, Kanuparthipadu, SPSR Nellore, Andhra Pradesh, India.

Please see the link here: https://stm.bookpi.org/RHMCS-V7/article/view/10006

Utility of Exponential Diophantine Equation 3x + by= cz | Chapter 1 | Novel Research Aspects in Mathematical and Computer Science Vol. 6

 

For all polynomial equations with integer coefficients and related unknowns assumed to be rational integers at this time, we employ the Diophantine equation. This concept is frequently expanded to include any kind of equation involving numbers and having integer unknowns. Fermat's equation xn + bn= cn, where x, b, c, and n > 3 are unidentified positive integers, serves as an illustrative example. When one or more exponents are unknown, the phrase "exponential Diophantine equation" is frequently used. Consider now that here, where min c > 1, b and c are positive integers with fixed coprime. Every positive number solution (x, y, and z) to the equation 3x + by = cz is categorised in this portion of the research paper.

Additionally, we must demonstrate that, if c = b+ 3, the equation has only positive integer solutions, i.e. (x, y, z) = (3, 2, 2), with the exception of (b, x, y, z) = (3, 3, 2, 2) and (3r -1, r +3, 3, 3), where r is a positive integer number of r >= 3.

Author(s) Details:

S. P. Behera,
Department of Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India.

Please see the link here: https://stm.bookpi.org/NRAMCS-V6/article/view/7760   

About Diophantine Equations z^2=(9^2-4)y^2-(4^2) | Chapter 10 | Recent Recent Advances in Mathematical Research and Computer Science Vol. 8

 The diophantine equation z2=(92-4)y2-(4) and its solutions are discussed. Not all of the Horadam numbers (H n,N n) where nN* and H n, N n Horadam numbers built using a second order recurrence have solutions. We demonstrate the connection between Qmatrices and the conic relation.

Author(S) Details

Serge Perrine
5 Rue du Bon Pasteur, 57070 Metz, France.

View Book:- https://stm.bookpi.org/RAMRCS-V8/article/view/5751

Study on Clean Matrices in M2(Z) | Chapter 01 | Recent Advances in Mathematical Research and Computer Science Vol. 7

 

Author(S) Details

K. N. Rajeswari
School of Mathematics, Vigyan Bhawan Khandwa Road, Indore–452 017, India.

Rafia Aziz
Government Girls College, Khargone, India.

View Book:- https://stm.bookpi.org/RAMRCS-V7/article/view/5486

Integral Solutions of the Binary Quadratic Diophantine Equation x - 2xy -y + 2x +14y= 72 | Chapter 08 | Recent Advances in Mathematical Research and Computer Science Vol. 2

 

The binary quadratic equation is discussed in this chapter x2 - 2xy - y2 + 2x + 14y = 72 The non-zero unique integer solutions of a hyperbola are investigated. We also get a list of its integral solutions and show a few intriguing relationships between them. The recurrence relations that the solutions x and y satisfy are found.

Author(S) Details

C. Saranya
Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli, Taminadu, India

G. Janaki
Department of Mathematics, Cauvery College for Women (Autonomous), (Affiliated to Bharathidasan University), Tiruchirappalli, Taminadu, India.

View Book:- https://stm.bookpi.org/RAMRCS-V2/article/view/4455