Markoff–Rosenberger triples in arithmetic progression

On Triples in Arithmetic Progression

Avoiding triples in arithmetic progression ∗

Some patterns cannot be avoided ad infinitum. A well-known example of such a pattern is an arithmetic progression in partitions of natural numbers. We observed that in order to avoid arithmetic progressions, other patterns emerge. A visualization is presented that reveals these patterns. We capitalize on the observed patterns by constructing techniques to avoid arithmetic progressions. More for...

Markoff-Rosenberger triples in arithmetic progression

Article history: Received 22 March 2012 Accepted 12 November 2012 Available online 27 November 2012

Markoff–rosenberger Triples in Geometric Progression

We study solutions of the Markoff–Rosenberger equation ax + by + cz = dxyz whose coordinates belong to the ring of integers of a number field and form a geometric progression.

Primes in arithmetic progression

Prime numbers have fascinated people since ancient times. Since the last century, their study has acquired importance also on account of the crucial role played by them in cryptography and other related areas. One of the problems about primes which has intrigued mathematicians is whether it is possible to have long strings of primes with the successive primes differing by a fixed number, namely...