a. If p is a prime number and a is a positive integer, how
Chapter 9, Problem 31E(choose chapter or problem)
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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