Facebook Instagram Twitter RSS Feed PodBean Back to top on side

An extension of Babbage's criterion for primality

In: Mathematica Slovaca, vol. 63, no. 6
Romeo Meštrović

Details:

Year, pages: 2013, 1179 - 1182
Keywords:
Babbage's criterion for primality, Lucas' theorem, congruence, prime power
About article:
Let $n>1$ and $k>1$ be positive integers. We show that if

$$ {n+m\choose n}\equiv 1\pmod{k} $$

for each integer $m$ with $0≤ m≤ n-1$, then $k$ is a prime and $n$ is a power of this prime. In particular, this assertion under the hypothesis that $n=k$ implies that $n$ is a prime. This was proved by Babbage, and thus our result may be considered as a generalization of this criterion for primality.
How to cite:
ISO 690:
Meštrović, R. 2013. An extension of Babbage's criterion for primality. In Mathematica Slovaca, vol. 63, no.6, pp. 1179-1182. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0164-8

APA:
Meštrović, R. (2013). An extension of Babbage's criterion for primality. Mathematica Slovaca, 63(6), 1179-1182. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0164-8
About edition: