One interesting family of diophantine triplets

Deshpande, M. N.

doi:10.1080/002073902753586337

Cited by 10 publications

(5 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The book [6] written by Dickson, has many crucial results on number theory and group theory. Deshpande [5] created Diophantine triples considering a recurrence relation in the terms of a special sequence. Dujella and Jurasic [7] defined the some types of regular Diophantine m-tuples and obtained significant results for them.…”

Section: Introductionmentioning

confidence: 99%

On some particular regular Diophantine 3-tuples

Özer¹,

Çiloğlu²

2019

Math. Nat. Sci.

View full text Add to dashboard Cite

Diophantine n-tuple where n=3 is called as a Diophantine triple. It means that Diophantine triple is a set of three positive integers satisfying special condition. For example, {a, b, c} is called a D(k)-Diophantine triple if multiplying of any two different of them plus k is a perfect square integer where k is an integer. In this work, we take in consideration some kind of regular D(±3 3)-Diophantine triples. We demonstrate that such sets can not be extendible to D(±3 3)-Diophantine quadruple by using algebraic methods such as classical Pell equations solutions, solutions of ux 2 + vy 2 = w Diophantine equations where u, v, w ∈ Z, factorization in the set of integers, and so on. Besides, we obtain some notable characteristic properties for such sets.

show abstract

Section: Introductionmentioning

confidence: 99%

On some particular regular Diophantine 3-tuples

Özer¹,

Çiloğlu²

2019

Math. Nat. Sci.

View full text Add to dashboard Cite

show abstract

“…[1][2][3] has been referred for multitudinal ideas on number theory. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] has been studied for numerous ideas on diophantine triples. In this paper we attempt to explicate dio 3-tuples from truncated octahedral number of different ranks.…”

Section: Introductionmentioning

confidence: 99%

Explication of Dio 3 -Tuples from Truncated Octahedral Number-I

Saranya¹

2018

IJRASET

View full text Add to dashboard Cite

show abstract

“…[1][2][3] has been studied for basic ideologies. [3][4][5][6][7][8][9][10][11][12][13][14][15] has been referred for various concepts and findings of Diophantine triples and quadruples. Recently in [16] special dio 3-tuples is constructed from n n Gno CC .…”

Section: Introductionmentioning

confidence: 99%