On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
نویسندگان
چکیده
In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions Binet formulas for these quaternions investigating some properties among them.
منابع مشابه
Gaussian Mersenne and Eisenstein Mersenne primes
The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
متن کاملMersenne and Fermat Numbers
The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
متن کاملGeneralised Mersenne Numbers Revisited
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked....
متن کاملArtin Reciprocity and Mersenne Primes
On March 3, 1998, the centenary of Emil Artin was celebrated at the Universiteit van Amsterdam. This paper is based on the two morning lectures, enti-tled`Artin reciprocity and quadratic reciprocity' and`Class eld theory in practice', which were delivered by the authors. It provides an elementary introduction to Artin reciprocity and illustrates its practical use by establishing a recently obse...
متن کاملMersenne Factorization Factory
We present new factors of seventeen Mersenne numbers, obtained using a variant of the special number field sieve where sieving on the algebraic side is shared among the numbers. It reduced the overall factoring effort by more than 50%. As far as we know this is the first practical application of Coppersmith’s “factorization factory” idea. Most factorizations used a new double-product approach t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Baghdad Science Journal
سال: 2023
ISSN: ['2078-8665', '2411-7986']
DOI: https://doi.org/10.21123/bsj.2023.8429