Special Dio 3-Tuples Involving Octagonal Pyramidal Numbers | Chapter 8 | Explorations in Diophantine Equations

 This chapter tries to build special Dio 3-tuples that satisfy the property that the product of any two of the triple's members subtracted by a non-zero integer or a polynomial with integer coefficients is a perfect square. The special Dio 3-tuples from octagonal pyramidal numbers of various ranks are also presented in each of the three parts along with the relevant features.

Author(s) Details:

C. 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.

R. Janani,
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/12435

Some Non-Extendable Special Dio 3-Tuples Involving Heptagonal Pyramidal Numbers | Chapter 5 | Explorations in Diophantine Equations

 In this chapter, we look for three particular polynomials with integer coefficients to such an extent that the product of any two numbers subtracted by a non-zero number (or polynomials with integer coefficients) is a perfect square. This chapter aims at constructing special dio 3-tuples where the product of any two members of the triple with the subtraction of a non-zero integer or a polynomial with integer coefficients satisfies the required property.

Author(s) Details:

C. 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.

P. Chitra,
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/12432