Ergebnisse über die Teiler der Folgen (a^n+1)
FakultätenFakultät für Mathematik und Wirtschaftswissenschaften
We define the set P_a as the divisors of a^n+1 where a is a fixed natural number and n is any natural number. One is interested in criteria to find out if a certain number d is in the set P_a or not. This question is very related to the term of the multiplicative order in Z/dZ. The author shows that it is only necessary to know about the primes in P_a and then one can easily check if any number d is in P_a or not. The main idea of the work is to look at certain similarities between the set P_a and the set of prime numbers. One can formulate statement for P_a-numbers which is very similar to the Goldbach´s conjecture and twin prime conjecture for prime numbers. The last part of this thesis deals with the set Q_d which contains all bases a with a^n+1 is divisible by d for a certain n. Looking for sets Q_d with "a maximum amount of elements" leads to the unsolved problem of Fermat prime numbers 2^(2^n)+1.
Erstellung / Fertigstellung
Normierte SchlagwörterZahlentheorie [GND]
Number theory [LCSH]