Values of the Euler and Carmichael Functions which are Sums of Three Squares

Integers ◽  
2011 ◽  
Vol 11 (2) ◽  
Author(s):  
Paul Pollack
Keyword(s):  
Sums Of Three Squares

AbstractLet

Quaternions and Sums of Three Squares

1942 ◽  
Vol 64 (1/4) ◽  
pp. 503 ◽  
Author(s):  
Gordon Pall
Keyword(s):  
Sums Of Three Squares

scholarly journals Sums of smooth squares

2009 ◽  
Vol 145 (6) ◽  
pp. 1401-1441 ◽  
Author(s):  
V. Blomer ◽  
J. Brüdern ◽  
R. Dietmann
Keyword(s):  
Lower Bound ◽  
Asymptotic Formula ◽  
Natural Number ◽  
Related Problem ◽  
Order Of Magnitude ◽  
Sums Of Three Squares

AbstractLet R(n,θ) denote the number of representations of the natural number n as the sum of four squares, each composed only with primes not exceeding nθ/2. When θ>e−1/3 a lower bound for R(n,θ) of the expected order of magnitude is established, and when θ>365/592, it is shown that R(n,θ)>0 holds for large n. A similar result is obtained for sums of three squares. An asymptotic formula is obtained for the related problem of representing an integer as the sum of two squares and two squares composed of small primes, as above, for any fixed θ>0. This last result is the key to bound R(n,θ) from below.

scholarly journals Arithmetic behaviour of the sums of three squares

1987 ◽  
Vol 27 (3) ◽  
pp. 273-284 ◽  
Author(s):  
A. Arenas ◽  
P. Bayer
Keyword(s):  
Sums Of Three Squares
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