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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 04 > No. 3

 
   

On Generalized Fermat Numbers 32n + 1

PP: 307-313
Author(s)
Amin Witno,
Abstract
The Fermat numbers F(n) = 22n + 1 have been studied to great extents as far as primality and factorization are concerned. The generalized Fermat numbers are those of the form Fa(n) = a2n + 1, which raise similar interests when a is an even number. If a is odd, of course, Fa(n) would be divisible by 2. In this paper, we investigate the behaviour of the numbers En = F3(n)/2 and present an initial primality test for En given that En−1 is known to be prime. Some ideas of research for future consideration are suggested.

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