Paper 2019/125
Combinatorial Primality Test
Maheswara Rao Valluri
Abstract
This paper provides proofs of the results of Laisant  Beaujeux: (1) If an integer of the form $n=4k+1$, $k>0$ is prime, then $\left(\begin{array}{c}n1\\m\end{array}\right)\equiv1(mod\,n),m=\frac{n1}{2}$, and (2) If an integer of the form $n=4k+3$, $k\geq0$ is prime, then $\left(\begin{array}{c}n1\\m\end{array}\right)\equiv1(mod\,n),m=\frac{n1}{2}$. In addition, the author proposes important conjectures based on the converse of the above theorems which aim to establish primality of $n$. These conjectures are scrutinized by the given combinatorial primality test algorithm which can also distinguish patterns of prime $n$ whether it is of the form $4k+1$ or $4k+3$.
Metadata
 Available format(s)
  withdrawn 
 Publication info
 Preprint. MINOR revision.
 Keywords
 LaisantBeaujeux pseudoprimesfactorialprimality
 Contact author(s)
 maheswara valluri @ fnu ac fj
 History
 20220824: withdrawn
 20190213: received
 See all versions
 Short URL
 https://ia.cr/2019/125
 License

CC BY