Solutions of ϕ(n) = ϕ(n + 1) for Euler's Function.

1978 ◽  
Vol 32 (144) ◽  
pp. 1326 ◽  
Author(s):  
D. S. ◽  
Robert Baillie
Keyword(s):  
Euler’S Function

scholarly journals The order of magnitude of the mth coefficients of cyclotomic polynomials

1985 ◽  
Vol 27 ◽  
pp. 143-159 ◽  
Author(s):  
H. L. Montgomery ◽  
R. C. Vaughan
Keyword(s):  
Cyclotomic Polynomial ◽  
Cyclotomic Polynomials ◽  
Order Of Magnitude ◽  
Euler’S Function ◽  
Image Position

We define the nth cyclotomic polynomial Φn(z) by the equationand we writewhere ϕ is Euler's function.Erdös and Vaughan [3] have shown thatuniformly in n as m-→∞, whereand that for every large m

Euler's?-function in the context of I? 0

1995 ◽  
Vol 34 (3) ◽  
pp. 197-209
Author(s):  
Marc Jumelet
Keyword(s):  
Euler’S Function

On the Equations xn±yn = zm

1970 ◽  
Vol 54 (388) ◽  
pp. 138-139
Author(s):  
R. G. Beerensson
Keyword(s):  
Primitive Root ◽  
Euler’S Function

1. We determine first an infinity of solutions of the equation x n-yn=zm when m, n are relatively prime. Let p be an odd prime; then q= p m has a primitive root g, say, and so, if ϕ is Euler's function, x= g ϕ(q) satisfies x n= gnϕ(q)) = l (mod q).

Popular values of Euler's function

Mathematika ◽  
1980 ◽  
Vol 27 (1) ◽  
pp. 84-89 ◽  
Author(s):  
Carl Pomerance
Keyword(s):  
Euler’S Function

Density Bounds for Euler's Function

1972 ◽  
Vol 26 (119) ◽  
pp. 779
Author(s):  
Charles R. Wall
Keyword(s):  
Euler’S Function
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