Question 1 4 pts (TCO 5) If b|a, we say that b is a _____ of a. residue group di

Question

Question 1
4 pts
(TCO 5) If b|a, we say that b is a _____ of a.

residue

group

divisor

modulus

Question 2
4 pts
(TCO 5) In the context of abstract algebra, we are usually not interested in evaluating a polynomial for a particular value of x. To emphasize this point, the variable x is sometimes referred to as the _____.

monic

constant

indeterminate

coefficient

Question 3
4 pts
(TCO 5) As a _____ relation, mod expresses that two arguments have the same remainder with respect to a given modulus.

finite

monic

congruence

cyclic

Question 4
4 pts
(TCO 5) If p is prime and a is a positive integer, then ap = a(mod p) is an alternative form of _____ theorem.

Rijndael’s

Vigenere’s

Euler’s

Fermat’s

Question 5
4 pts
(TCO 5) Two numbers are relatively prime if they have _____ prime factors in common.

some

zero

multiple

all

Question 6
5 pts
(TCO 5) The procedure TEST takes a candidate integer n as input and returns the result _____ if n may or may not be a prime.

discrete

composite

inconclusive

primitive

Question 7
5 pts
(TCO 5) Division requires that each nonzero element have a(n) _____ inverse.

multiplicative

divisional

subtraction

addition

Explanation / Answer

Solution:

Question 1

If b | a, we say that b is a divisor of a.

Explanation: If a | b, it can be said that b divides a.

Question 2

In the context of abstract algebra, we are usually not interested in evaluating a polynomial for a particular value of x. To emphasize this point, the variable x is sometimes referred to as the indeterminate.

Explanation: The operations that are involved in polynomial arithmetic are addition, subtraction and multiplication. There are various values of any variable at which the evaluation of a polynomial is not required to be performed, so polynomial arithmetic is not supported for all values of a variable. Such variables are called indeterminate.

Question 3

As a congruence relation, mod expresses that two arguments have the same remainder with respect to a given modulus.

Explanation: Modulo congruence means that if two arguments are given, then they have the same remainder with respect to a given modulus. For example, 11 mod 5 = 16 mod 5 = 1.

Question 4

If p is prime and a is a positive integer, then a p=a(mod)p is an alternative form of Fermat’s theorem

Explanation: According to Fermat’s little theorem, if p is prime, then for all a. There is another alternative form of the Fermat’s theorem according to which where p is the prime and a is an integer not divisible by p

Question 5:

Two numbers are relatively prime if they have zero prime factors in common.

Explanation: The prime numbers are the numbers that have no common factors except 1.

Question 6:

The procedure TEST takes a candidate integer n as input and returns the result composite if n may or may not be a prime.

Explanation:

If the candidate integer n is taken as the input and n is not prime, then the integer will be composite.

Question 7

Division requires that each non-zero element have a(n) multiplicative inverse.

Explanation: Every non-zero element has a multiplicative inverse.

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