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DETAILS MY NOTES The number 42 has the prime factorization 2· 3·7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1. 42, 2· 21, 3 · 14, and 6 · 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 858 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P,PaPa, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f,. Then f, corresponds to a subset of {p,, P2» Pav Pa}, and f, corresponds to the complement of that subset.) (c) If n = P,P2P3P4P5, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n = P,P2 Pu where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?

DETAILS MY NOTES The number 42 has the prime factorization 2· 3·7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1. 42, 2· 21, 3 · 14, and 6 · 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 858 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P,PaPa, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f,. Then f, corresponds to a subset of {p,, P2» Pav Pa}, and f, corresponds to the complement of that subset.) (c) If n = P,P2P3P4P5, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n = P,P2 Pu where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. EPPDISCMATH5 9.5.024. DETAILS MY NOTES The number 42 has the prime factorization 2· 3· 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1· 42, 2 · 21, 3· 14, and 6 · 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 858 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, p,PaPa where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f,. Then f, corresponds to a subset of {p,, P2, P3, Pa}, and f, corresponds to the complement of that subset.) (c) If n = p, p,P3PAP5, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n = p, p, ... P, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
Transcribed Image Text:2. EPPDISCMATH5 9.5.024. DETAILS MY NOTES The number 42 has the prime factorization 2· 3· 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1· 42, 2 · 21, 3· 14, and 6 · 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 858 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, p,PaPa where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f,. Then f, corresponds to a subset of {p,, P2, P3, Pa}, and f, corresponds to the complement of that subset.) (c) If n = p, p,P3PAP5, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n = p, p, ... P, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
9. DETAILS EPPDISCMATH5 7.1.006. MY NOTES Find functions defined on the set of nonnegative integers that can be used to define the sequences whose first six terms are given below. (a) 1 3' 1 1 1 ,6 12' 15 18 f(n) = for each integer 2 1 (b) 0, -8, 16, –24, 32, –40 f(n) = for each real number 20 Viewing Saved Work Revert to Last Response
Transcribed Image Text:9. DETAILS EPPDISCMATH5 7.1.006. MY NOTES Find functions defined on the set of nonnegative integers that can be used to define the sequences whose first six terms are given below. (a) 1 3' 1 1 1 ,6 12' 15 18 f(n) = for each integer 2 1 (b) 0, -8, 16, –24, 32, –40 f(n) = for each real number 20 Viewing Saved Work Revert to Last Response
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