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On A Theorem of Niven

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University, Ottawa
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In 1940, I. Niven [2] proved that the gaussian integer z = x + iy is the sum of two squares of gaussian integers if, and only if, y is even and not both of 1/2x and 1/2y are rational odd integers. In this note we calculate the total number g2(z) of representations of z in this form.

1

where a, b, c, d are rational integers, if and only if

2

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 573 - 578
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Leahey, W. J., A note on a theorem of I. Niven. Proc. Amer. Math. Soc, 16 (1966), 1130-1131.Google Scholar
2. Niven, I., Integers of quadratic fields as sums of squares. Trans. Amer. Math. Soc, 48 (1944), 405-417.Google Scholar