NUMBER THEORY, An approach to its open problems – George G. Katsanevakis

Description

Number theory is considered the queen of mathematics and is famous by the multitude of open / unsolved problems whose wording is understood even by a high school student.

Questions such as:

a) Are the twin prime numbers infinite?

b) Is each even number written as the sum of two prime numbers?

(Goldbach guess).

c) Does the Fibonacci sequence have infinite prime numbers among its terms ?

d) How many prime numbers are there between the squares of two consecutive integers?

e) Are even perfect numbers infinite?

f) Are there odd perfect numbers?

g) Can Fermat’s last theorem be solved by elementary mathematics?

h) After each first number, how much -at most- do we have to search to find the next one?

And much more remains unanswered even though mathematical experience prescribes the answer to them.

This paper is a popularized attempt to approach, investigate and supervise some open problems of number theory.

The knowledge required to understand them is of the traditional lyceum. That is why the way of presenting the problems is the simplest possible with many explanations and examples. Some problems we consider to have comprehensive evidence while in others the approach, investigation and supervision is done with unidirectional tables unidirectionally defined.

This work is aimed not only at mathematicians and science students, but also at intellectually restless readers , who are nostalgic for the beauty of high school mathematics.

Essentially, readers are given an opportunity to familiarize themselves with the prime numbers with the aim of possibly engaging with them.