Polynomials which take Gaussian integer values at Gaussian integers
نویسندگان
چکیده
منابع مشابه
Gaussian Integers
We will investigate the ring of ”Gaussian integers” Z[i] = {a + bi | a, b ∈ Z}. First we will show that this ring shares an important property with the ring of integers: every element can be factored into a product of finitely many ”primes”. This result is the key to all the remaining concepts in this paper, which includes the ring Z[i]/αZ[i], analogous statements of famous theorems in Z, and q...
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Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rat...
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متن کاملThe Gaussian Integers
Since the work of Gauss, number theorists have been interested in analogues of Z where concepts from arithmetic can also be developed. The example we will look at in this handout is the Gaussian integers: Z[i] = {a + bi : a, b ∈ Z}. Excluding the last two sections of the handout, the topics we will study are extensions of common properties of the integers. Here is what we will cover in each sec...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1977
ISSN: 0022-314X
DOI: 10.1016/0022-314x(77)90012-9