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# a. If p is a prime number and a is a positive integer, how

## Problem 31E Chapter 9.2

Discrete Mathematics with Applications | 4th Edition

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Discrete Mathematics with Applications | 4th Edition

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Problem 31E

a. If p is a prime number and a is a positive integer, how many distinct positive divisors does pa have?

b. If p and q are distinct prime numbers and a and b are positive integers, how many distinct positive divisors does pa qb have?

c. If p, q, and r are distinct prime numbers and a, b, and c are positive integers, how many distinct positive divisors does paqbrc have?

d. If p1, p2, …, pm are distinct prime numbers and a1, a2, …, am are positive integers, how many distinct positive divisors does  have?

e. What is the smallest positive integer with exactly 12 divisors?

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##### ISBN: 9780495391326

The full step-by-step solution to problem: 31E from chapter: 9.2 was answered by Sieva Kozinsky, our top Math solution expert on 07/19/17, 06:34AM. This full solution covers the following key subjects: Positive, distinct, divisors, prime, integers. This expansive textbook survival guide covers 131 chapters, and 5076 solutions. Since the solution to 31E from 9.2 chapter was answered, more than 223 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics with Applications , edition: 4th. Discrete Mathematics with Applications was written by Sieva Kozinsky and is associated to the ISBN: 9780495391326. The answer to “a. If p is a prime number and a is a positive integer, how many distinct positive divisors does pa have?b. If p and q are distinct prime numbers and a and b are positive integers, how many distinct positive divisors does pa qb have?c. If p, q, and r are distinct prime numbers and a, b, and c are positive integers, how many distinct positive divisors does paqbrc have?d. If p1, p2, …, pm are distinct prime numbers and a1, a2, …, am are positive integers, how many distinct positive divisors does have?e. What is the smallest positive integer with exactly 12 divisors?” is broken down into a number of easy to follow steps, and 104 words.

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