منابع مشابه
On Generalized Elite Primes
A prime number p is called b-elite if only finitely many generalized Fermat numbers Fb,n = b 2 + 1 are quadratic residues to p. So far, only the case b = 2 was subjected to theoretical and experimental researches by several authors. Most of the results obtained for this special case can be generalized for all bases b > 2. Moreover, the generalization allows an insight to more general structures...
متن کاملun 2 00 9 Base - 3 Repunit Primes and the Cantor Set
The middle-third Cantor set C3 is a fractal consisting of all the points in [0, 1] which have non-terminating base-3 representations involving only the digits 0 and 2. I prove that all prime numbers p > 3 whose reciprocals belong to C3 must be base-3 repunit primes, and, conversely, that the reciprocals of all base-3 repunit primes must be in C3. This one-one correspondence appears to be unique...
متن کاملRepunit Lehmer numbers
A Lehmer number is a composite positive integer n such that φ(n) | n− 1. In this paper, we show that given a positive integer g > 1 there are at most finitely many Lehmer numbers which are repunits in base g, and they are all effectively computable. Our method is effective and we illustrate it by showing that there is no such Lehmer number when g ∈ [2, 1000]. 2000 Mathematics Subject Classifica...
متن کاملVerifying Two Conjectures on Generalized Elite Primes
A prime number p is called b-elite if only finitely many generalized Fermat numbers Fb,n = b 2 + 1 are quadratic residues modulo p. Let p be a prime. Write p − 1 = 2h with r ≥ 0 and h odd. Define the length of the b-Fermat period of p to be the minimal natural number L such that Fb,r+L ≡ Fb,r (mod p). Recently Müller and Reinhart derived three conjectures on b-elite primes, two of them being th...
متن کاملLarge primes in generalized Pascal triangles
In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1993-1185243-9