MATH 521A: Abstract Algebra Homework 7 Solutions 1. Consider
... different ones, such as f (x) = (x + 2)(x + x + 1), and 10 ways of picking the square of one, such as f (x) = (x2 + 2)2 . Hence there are 45 + 10 = 55 answers to this question. 6. Factor x7 − x as a product of irreducibles in Z7 [x]. By Fermat’s Little Theorem, x7 ≡ x (mod 7), for all integer x. Hen ...
... different ones, such as f (x) = (x + 2)(x + x + 1), and 10 ways of picking the square of one, such as f (x) = (x2 + 2)2 . Hence there are 45 + 10 = 55 answers to this question. 6. Factor x7 − x as a product of irreducibles in Z7 [x]. By Fermat’s Little Theorem, x7 ≡ x (mod 7), for all integer x. Hen ...
CHAP11 Z2 Polynomials
... invent solutions for this polynomial. A new “imaginary” number “i” was introduced to provide a solution and we combined this number with the existing real numbers to form complex numbers x + iy. We were then able to do arithmetic in this larger system just using the relation i2 = 1. It turned out t ...
... invent solutions for this polynomial. A new “imaginary” number “i” was introduced to provide a solution and we combined this number with the existing real numbers to form complex numbers x + iy. We were then able to do arithmetic in this larger system just using the relation i2 = 1. It turned out t ...
PPT
... Suppose that the minimum distance between points is at least d, what is the maximum number of points that can be packed in a ball of radius d? ...
... Suppose that the minimum distance between points is at least d, what is the maximum number of points that can be packed in a ball of radius d? ...
1 FINITE FIELDS 7/30 陳柏誠 2 Outline: Groups, Rings, and Fields
... There are only two such polynomials: (x3 + x2 + 1) and (x3 + x + 1). Using the latter, Table 4.7 shows the addition and multiplication tables for GF(23). Note that this set of tables has the identical structure to those of Table 4.6. Thus, we have succeeded in finding a way to define a field of orde ...
... There are only two such polynomials: (x3 + x2 + 1) and (x3 + x + 1). Using the latter, Table 4.7 shows the addition and multiplication tables for GF(23). Note that this set of tables has the identical structure to those of Table 4.6. Thus, we have succeeded in finding a way to define a field of orde ...