“NUMBER THEORY One approach of open problems” Georgios G. Katsanevakis The theory of numbers is considered the queen of mathematics and is famous by the number of open / unresolved problems of which the formulation is understood even by a high school student. Questions like: a) Are the twin prime numbers infinite? b) Every even number is written as the sum of two primes? (GoldBach guess). c) Does Fibonacci sequence of numbers have between its terms infinite prime numbers? d) How many prime numbers are between the squares of two consecutive integers? e) Are even perfect numbers infinite? f) Are there any odd perfect numbers? g) The last theorem of Fermat can be solved by elementary mathematics? h) After each first number how much – the maximum - we have to look to find the next one? and many other questions remain unanswered although the mathematical experience specifies the answer to them. The present paper is an effort of simplified approaching, expansion and inspection for some open number problems of the number theory. High School knowledge is required in order to understand them. For that reason and the presentation of these problems is the simpler as possible with many explanations and examples. We estimate that for some of these problems have complete proofs while at some others the approach, expansion and inspection has been done with uniquely tables single-mode defined. This work addresses not only math and science students, but also to spiritually anxious readers who miss the beauty of high school mathematics. Essentially giveς το readers an opportunity of familiarization with prime numbers with a view to possible involvement with them. Note: The problems of the theory of numbers: a. There are no odd perfect numbers b. An investigation of Fermat’s last theorem c. An approach to the Riemann Hypothesis have been published at volume 23/2 of the journal “International Journal of Mathematics, Game Theory and Algebra”. Georgios G. Katsanevakis is a civil engineer. He is the President of the Administrative Council of ANEK LINES SA. He was Prefect of Chania (1999 – 2006), Mayor of Chania (1983 – 1990) and President of Technical Chamber of West Crete (1975 – 1983).
Chania 2016 ISBN: 978-618-81875-5-9 Politistiki Etairia Kritis – Pyxida tis Polis Publications http://ekdoseis-pek.blogspot.gr/
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