Solved: a. If p is a prime number and a is a positive

Chapter 9, Problem 9.63

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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 paqb have? c. If p,q, andr are distinct prime numbers and a,b, andc arepositiveintegers,howmanydistinctpositivedivisors 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 pa1 1 pa2 2 pam m have? e. What is the smallest positive integer with exactly 12 divisors?

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