An Abelian Loop for Non-Composites

Raghavendra N. Bhat

doi:10.35834/2022/3402191

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arXiv · 2110.14716

An Abelian Loop for Non-Composites

Raghavendra N. Bhat

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Abstract

We define an abelian loop on a set $S$ consisting of 1 and all odd prime numbers with an operation $\bullet$, where for $a,b$ $\in$ $S$, $a$ $ \bullet$ $b$ is the smallest element of $S$ strictly larger than $|a-b|$. We use theorems and conjectures from number theory to prove properties of the loop and state analogous conjectures about the loop.

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BibTeX RIS

Raghavendra N. Bhat. 2021-10-27. An Abelian Loop for Non-Composites. https://doi.org/10.35834/2022%2F3402191

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