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.

scholarly journals Carmichael numbers in number rings

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

On the sum of the first n values of the Euler function

2014 ◽  
Vol 163 (3) ◽  
pp. 199-201 ◽  
Author(s):  
R. Balasubramanian ◽  
Florian Luca ◽  
Dimbinaina Ralaivaosaona
Keyword(s):  
Euler Function

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).

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