Carmichael numbers composed of primes from a Beatty sequence

2011 ◽  
Vol 125 (1) ◽  
pp. 129-137 ◽  
Author(s):  
William D. Banks ◽  
Aaron M. Yeager
Keyword(s):  
Carmichael Numbers ◽  
Beatty Sequence

scholarly journals Carmichael numbers in number rings

2008 ◽  
Vol 128 (4) ◽  
pp. 910-917 ◽  
Author(s):  
G. Ander Steele
Keyword(s):  
Carmichael Numbers

scholarly journals Extended Bounds of Beatty Sequence Associated with Primes

2019 ◽  
Vol 8 (6S3) ◽  
pp. 115-118
Keyword(s):  
Character Sums ◽  
Beatty Sequences ◽  
Composite Moduli ◽  
Beatty Sequence

This paper discusses on the estimation of character sums with respect to non-homogeneous Beatty sequences, over prime where , and is irrational. In particular, the bounds is found by extending several properties of character sums associated with composite moduli over prime. As a result, the bound of is deduced.

scholarly journals A certain power series associatedwith a Beatty sequence

1996 ◽  
Vol 76 (2) ◽  
pp. 109-129 ◽  
Author(s):  
Takao Komatsu
Keyword(s):  
Power Series ◽  
Beatty Sequence

scholarly journals Counting Carmichael numbers with small seeds

2010 ◽  
Vol 80 (273) ◽  
pp. 437-442
Author(s):  
Zhenxiang Zhang
Keyword(s):  
Carmichael Numbers

On Numbers Analogous to the Carmichael Numbers

1977 ◽  
Vol 20 (1) ◽  
pp. 133-143 ◽  
Author(s):  
H. C. Williams
Keyword(s):  
Carmichael Numbers ◽  
Image Position ◽  
Composite Integer

A base a pseudoprime is an integer n such that1A Carmichael number is a composite integer n such that (1) is true for all a such that (a, n ) = l. It was shown by Carmichael [1] that, if n is a Carmichael number, then n is the product of k(>2) distinct primes P1,P2,P3, … Pk, and Pi-1|n-1(i=1, 2, 3, …, k).

Carmichael Numbers with a Square Totient

2009 ◽  
Vol 52 (1) ◽  
pp. 3-8 ◽  
Author(s):  
W. D. Banks
Keyword(s):  
Euler Function ◽  
Carmichael Numbers

AbstractLet φ denote the Euler function. In this paper, we show that for all large x there are more than x0.33 Carmichael numbers n ⩽ x with the property that φ(n) is a perfect square. We also obtain similar results for higher powers.

Irregularities in the Distribution of Prime Numbers in a Beatty Sequence

2019 ◽  
Vol 63 (4) ◽  
pp. 738-743
Author(s):  
Janyarak Tongsomporn ◽  
Jörn Steuding
Keyword(s):  
Finite Type ◽  
Irrational Number ◽  
Prime Numbers ◽  
Positive Real ◽  
Beatty Sequence

AbstractWe prove irregularities in the distribution of prime numbers in any Beatty sequence ${\mathcal{B}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$, where $\unicode[STIX]{x1D6FC}$ is a positive real irrational number of finite type.

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