On prime divisors of Mersenne numbers
نویسندگان
چکیده
منابع مشابه
Sums of Prime Divisors and Mersenne Numbers
The study of the function β(n) originated in the paper of Nelson, Penney, and Pomerance [7], where the question was raised as to whether the set of Ruth-Aaron numbers (i.e., natural numbers n for which β(n) = β(n+ 1)) has zero density in the set of all positive integers. This question was answered in the affirmative by Erdős and Pomerance [5], and the main result of [5] was later improved by Po...
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Let Bn (n = 0, 1, 2, . . .) denote the usual n-th Bernoulli number. Let l be a positive even integer where l = 12 or l ≥ 16. It is well known that the numerator of the reduced quotient Bl/l is a product of powers of irregular primes. Let (p, l) be an irregular pair with p below 12 million. We show that for every r ≥ 1 the congruence Bmr/mr ≡ 0 (mod p ) has a unique solution for mr where l ≡ mr ...
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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....
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1991
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-57-3-267-281