A Certain Type of Regular Diophantine Triples and Their Non-Extendability

Özer, Özen

doi:10.12691/tjant-7-2-4

Cited by 1 publication

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. a m ) is called a Diophantine m-tuple if (a i a j + 1) is a perfect square for all 1 ≤ i ≤ j ≤ m. For a widespread assessment of numerous articles one can study (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) . In this manuscript, the particular forms of 4-tuples {(α 1 , β 1 , γ 1 , p 1 ) , (β 1 , γ 1 , γ 2 , q 1 ) , (γ 1 , γ 2 , γ 3 , s 1 ) , (γ 2 , γ 3 , γ 4 ,t 1 ) .…”

Section: Introductionmentioning

confidence: 99%

Establishment of Order of 4-Tuples Concerning Familiar Polynomials with Captivating Condition

Pandichelvi,

Umamaheswari

2023

IJST

View full text Add to dashboard Cite

Objectives: Finding the feature of a number pattern is a fascinating area of current research. There are numerous features, one of which is that the Area by Perimeter of a Pythagorean triangle is a nasty number, figurate number, and so on. This manuscript aims to identify the precise sorts of 4-tuples combining Legendre polynomials and Probabilist's Hermite polynomials in which the product of any two polynomials is added by one square to another polynomial. Method: By using specific transformation, the assumption can be turned into a universal second-degree equation with two variables known as the Pell equation. The solution to this equation yields 3-tuples and their extension into 4-tuples from 2-tuples in a precise manner, as explained. Findings: This paper describes some types of 4-tuples involving Legendre polynomials and Probabilist's Hermite polynomials in which the product of any two polynomials is added by the number one in any 4-tuple results in the square of an alternate polynomial. Novelty: A Python program is achieved for displaying all 4-tuples with the numerical values of the specified unknown combination with the special property.

show abstract