A Generalised Stern-Brocot Tree from Regular Diophantine Quadruples
Philip Gibbs
Abstract
Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which can be constructed recursively. Some observations on these regular solutions are presented. In particular we see how factors of the four numbers satisfy relations which generalise the Stern-Brocot Tree. There is also an update on the search for rational Diophantine sextuples with five new examples.
Create a lesson
Related papers
Value distribution of multiplicative functions along linear fractional sequences
Sun-Kai Leung
Delta theory of Anderson Modules II: Hodge-Pink structure
Sudip Pandit, Arnab Saha
Integers divisible by a shifted prime in a given interval
Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt et al.
On Piatetski-Shapiro primes from almost primes
Yuhua Zhao, Jinjiang Li, Linji Long et al.
On Consecutive Non-primitive Elements over Finite Fields
Bidushi Sharma, Dhiren Kumar Basnet
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu