6. The number of divisors that a number has is very easy to calculate if the...
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6. The number of divisors that a number has is very easy to calculate if the number is given in prime-power decomposition form. If n = p¹.p2² then the number of divisors of n is ak Pk 2 (a₁ + 1) (a2 + 1).. • (ak + 1). For example, the number of divisors of 172872 = 2³3274 is (3+1) (2+1) (4+1)=4.3.5 = 60 The proof of it is a rather simple counting argument. Using this, answer the following questions. (a) Characterize the numbers that have 4 divisors (b) Characterize those numbers that have exactly 6 divisors. (c) Characterize those numbers that have a prime number of divisors (d) Give the formulas that will generate positive integers that have exactly 12 divisors. 6. The number of divisors that a number has is very easy to calculate if the number is given in prime-power decomposition form. If n = p¹.p2² then the number of divisors of n is ak Pk 2 (a₁ + 1) (a2 + 1).. • (ak + 1). For example, the number of divisors of 172872 = 2³3274 is (3+1) (2+1) (4+1)=4.3.5 = 60 The proof of it is a rather simple counting argument. Using this, answer the following questions. (a) Characterize the numbers that have 4 divisors (b) Characterize those numbers that have exactly 6 divisors. (c) Characterize those numbers that have a prime number of divisors (d) Give the formulas that will generate positive integers that have exactly 12 divisors.
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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