Results 241 to 250 of about 539,388 (277)

Exploring the Gaussian Integers

The Two-Year College Mathematics Journal, 1976
(1976). Exploring the Gaussian Integers. The Two-Year College Mathematics Journal: Vol. 7, No. 4, pp. 4-10.
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The Euclidean algorithm for Gaussian integers

1983
A theorem by Lame (1845) answers the following questions: given N, what is the maximum number of divisions, if the Euclidean algorithm is applied to integers u, v with N≥u≥n≥0? In this paper we give an analogous result for the Euclidean algorithm applied to Gaussian integers, that is, complex numbers a+bi, where a and b are integers.
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Gaussian Approximation Using Integer Sequences

2014
The need for generating samples that approximate statistical distributions within reasonable error limits and with less computational cost, necessitates the search for alternatives. In this work, we focus on the approximation of Gaussian distribution using the convolution of integer sequences.
Arulalan M. Rajan, Ashok Rao, R. Vittal Rao, H. S. Jamadagni   +3 more
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Gaussian Integers and Arctangent Identities for π

The American Mathematical Monthly, 2009
(2009). Gaussian Integers and Arctangent Identities for π. The American Mathematical Monthly: Vol. 116, No. 6, pp. 515-530.
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The probability of relative primality of Gaussian integers

1989
In this paper we generalize, to an arbitrary number field, the theorem which gives the probability that two integers are relatively prime. The probability that two integers are relatively prime is 1/ζ(2), where ζ is the Riemann zeta function and 1/ζ(2)=6/π2.
George E. Collins, Jeremy R. Johnson
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Sum of Divisors in a Ring of Gaussian Integers

Ukrainian Mathematical Journal, 2001
Summary: We construct an asymptotic formula for a summation function for \(\sigma_a(\alpha)\), where \(\sigma_a(\alpha)\) is the sum of the \(a\)-th powers of the norms of divisors of the Gaussian integer \(\alpha\) on an arithmetic progression \(\alpha\sim\alpha_0\pmod\gamma\) and in a narrow sector \(\phi_1\leq\operatorname {arg ...
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Primitive Pythagorean Triples of Gaussian Integers

Mathematics Magazine, 1986
(1986). Primitive Pythagorean Triples of Gaussian Integers. Mathematics Magazine: Vol. 59, No. 2, pp. 106-110.
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Dealing with categorical and integer-valued variables in Bayesian Optimization with Gaussian processes

Neurocomputing, 2020
Daniel Hernández-Lobato, Eduardo C Garrido-Merchán   +1 more
exaly  

Study of Safe Elliptic Curve Cryptography over Gaussian Integer

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2020
Tomoaki Kimura
exaly  

New Perfect Gaussian Integer Sequences of Period <i>pq</i>

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2013
Hui-Juan Zuo, Qiaoyan Wen
exaly