Suppose the integer 7a.11a+1 has 42 positive divisors. What is the value of a?Select one:a.5b.None of the othersc.21d.7e.6
Question
Solution 1
The number 7a.11a+1 can be rewritten as 7^a * 11^(a+1). The number of divisors of a number in prime factorization form (p1^e1 * p2^e2 * ... * pn^en) is (e1+1)(e2+1)...(en+1).
Given that 7a.11a+1 has 42 divisors, we can set up the equation (a+1)(a+2) = 42.
Solving this equation gives a = 5 or a = Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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