Relation between Lateral Surface Area of a Cube and Centered Polygonal Numbers | Chapter 12 | Explorations in Diophantine Equations

 With the help of the Bharamaguptha lemma, we endeavour to explore the lateral surface area of a cube with centred polygonal numbers. Along with that, explore ranks of centred polygonal numbers with their recurrence relations and the sides of a cube.

Author(s) Details:

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

A. Gowri Shankari,
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/12439

Some Non-Extendable Special Diophantine Triples Involving Nonagonal Pyramidal Numbers | Chapter 9 | Explorations in Diophantine Equations

 In this chapter, we discover the special Diophantine triples for the nonagonal pyramidal number with distinct ranks. The chapter mainly focuses on building three separate polynomials with integer coefficients (p, q, r) such as the multiple of any two components of the ensemble increased to their total and prolonged by a non-null integer (or a polynomial with integral coefficients) is a perfect square. In addition, the triple is not extended to a quadruple is analyzed. It is concluded that, we can explore for some other Special Diophantine triples for higher order Pyramidal numbers with equivalent fitting properties.

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.

Please see the link here: https://stm.bookpi.org/EDE/article/view/12436

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

The Negative Pell Equation y2 = 90x2 - 36: A Mathematical Observation | Chapter 3 | Research and Applications Towards Mathematics and Computer Science Vol. 4

 In this episode, we have presented infinitely many number solutions for the Diophantine equation, presented by hyperbola is given by y2 = 90x2 - 36 . The arched represented by the twofold quadratic equation y2 = 90x2 - 36 is resolved for finding its non-zero different integer solutions. A few entertaining relations among allure solutions are presented. Also, aware an integral solution of the likely hyperbola, integer answers for other choices of hyperbolas and parabolas are bestowed Also, employing the solutions of the likely equation, special Pythagorean trio is constructed. Diophantine equations enter place a wide variety; one can expect further options and ascertain the number solutions and appropriate features of those equatings.

Author(s) Details:

N. Anusheela,
Department of Mathematics, Government Arts College, Udhagamandalam, The Nilgiris-643 002, India.

Shreemathi Adiga,
Department of Mathematics, Government First Grade College, Koteshwara, Kundapura Taluk, Udupi-576222, Karnataka, India.

M. A. Gopalan,
Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620 002, Tamil Nadu, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V4/article/view/11811