Pairs of Sums of Three Squares of Integers Whose Product Has the Same Property

1980 ◽  
pp. 29-36 ◽  
Author(s):  
Olga Taussky
Keyword(s):  
Sums Of Three Squares

Quaternions and Sums of Three Squares

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

Two Equal Sums of Three Squares with Equal Products

1991 ◽  
Vol 98 (6) ◽  
pp. 527-529 ◽  
Author(s):  
John B. Kelly
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

scholarly journals Sums of three squares

1957 ◽  
Vol 8 (2) ◽  
pp. 316-316 ◽  
Author(s):  
N. C. Ankeny
Keyword(s):  
Sums Of Three Squares

A Correlated Digital Sum Problem Associated with Sums of Three Squares

1989 ◽  
Vol 21 (4) ◽  
pp. 369-374 ◽  
Author(s):  
A. H. Osbaldestin ◽  
P. Shiu
Keyword(s):  
Sums Of Three Squares
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