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

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Question 1 4 pts

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

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Question 2 4 pts

(TCO 5) With the understanding that remainders are allowed, we can say that polynomial division is possible if the coefficient set is a _____.

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Question 3 4 pts

(TCO 5) The congruence relation is used to define _____.

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Question 4 4 pts

(TCO 5) An important quantity in number theory referred to as _____ is defined as the number of positive integers less than n and relatively prime to n.

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Question 5 4 pts

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

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Question 6 5 pts

(TCO 5) The procedure TEST takes a candidate integer n as input and returns the result _____ if n is definitely not a prime.

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Question 7 5 pts

(TCO 5) A _____ is a set in which you can do addition, subtraction, multiplication, and division without leaving the set.

Explanation / Answer

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

(Here a and b are numbers , we also say b divides a, and write it as b|a)

2. With the understanding that remainders are allowed, we can say that polynomial division is possible if the coefficient set is a field .

3. The congruence relation is used to define residue classes .

(A congruence realtion ion a set of integers set integers, separates the set into two equivalent classes called residue classes)

4. An important quantity in number theory referred to as Euler’s Totient function is defined as the number of positive integers less than n and relatively prime to n.

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

6.  The procedure TEST takes a candidate integer n as input and returns the result composite if n is definitely not a prime.

7.  A field is a set in which you can do addition, subtraction, multiplication, and division without leaving the set.

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