Results 251 to 260 of about 391,951 (282)
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2003
The Gaussian integers ℤ[i] are the simplest generalization of the ordinary integers ℤ and they behave in much the same way. In particular, ℤ[i] enjoys unique prime factorization, and this allows us to reason about ℤ[i] the same way we do about Z. We do this because ℤ[i] is the natural place to study certain properties of ℤ.
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The Gaussian integers ℤ[i] are the simplest generalization of the ordinary integers ℤ and they behave in much the same way. In particular, ℤ[i] enjoys unique prime factorization, and this allows us to reason about ℤ[i] the same way we do about Z. We do this because ℤ[i] is the natural place to study certain properties of ℤ.
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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
1983A 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
2014The 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 +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
1989In 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, 2001Summary: 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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A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers
Electronics (Switzerland), 2020Freudenberger Jürgen +2 more
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Fourth power diophantine equations in Gaussian integers
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2018Farzali Izadi
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