Paper 2004/034
s(n) An Arithmetic Function of Some Interest, and Related Arithmetic
Gideon Samid
Abstract
Every integer n > 0 º N defines an increasing monotonic series of integers: n1, n2, ...nk, such that nk = nk +k(k1)/2. We define as s(m) the number of such series that an integer m belongs to. We prove that there are infinite number of integers with s=1, all of the form 2^t (they belong only to the series that they generate, not to any series generated by a smaller integer). We designate them as sprime integers. All integers with a factor other than 2 are not sprime (s>1), but are scomposite. However, the arithmetic s function shows great variability, lack of apparent pattern, and it is conjectured that s(n) is unbound. Two integers, n and m, are defined as scongruent if they have a common sseries. Every arithmetic equation can be seen as an expression without explicit unknowns  provided every integer variable can be replaced by any scongruent number. To validate the equation one must find a proper match of such members. This defines a special arithmetic, which appears well disposed towards certain cryptographic applications.
Metadata
 Available format(s)
 Category
 Foundations
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 number theory
 Contact author(s)
 samidg @ tx technion ac il
 History
 20040216: received
 Short URL
 https://ia.cr/2004/034
 License

CC BY
BibTeX
@misc{cryptoeprint:2004/034, author = {Gideon Samid}, title = {s(n) An Arithmetic Function of Some Interest, and Related Arithmetic}, howpublished = {Cryptology ePrint Archive, Paper 2004/034}, year = {2004}, note = {\url{https://eprint.iacr.org/2004/034}}, url = {https://eprint.iacr.org/2004/034} }