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ssible value of N. (7) (C) A student asks what the best way is to show if a number N is prime. What do you say? At first students think one has to try to divide N by all primes less than N and if none divide N evenly, then N is prime. But, a better way is to show by contradiction that if N = pq then one of p and q must be less than or equal to VN. Thus, when trying to determine if a number is prime, they need only check for prime divisors less than or equal to VN. Show how you would prove this result and help your students see how to use it to show that 143 s see how to use it to show th is not prime and that 569 is prime..

ssible value of N. (7) (C) A student asks what the best way is to show if a number N is prime. What do you say? At first students think one has to try to divide N by all primes less than N and if none divide N evenly, then N is prime. But, a better way is to show by contradiction that if N = pq then one of p and q must be less than or equal to VN. Thus, when trying to determine if a number is prime, they need only check for prime divisors less than or equal to VN. Show how you would prove this result and help your students see how to use it to show that 143 s see how to use it to show th is not prime and that 569 is prime..

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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ssible value of N. (7) (C) A student asks what the best way is to show if a number N is prime. What do you say? At first students think one has to try to divide N by all primes less than N and if none divide N evenly, then N is prime. But, a better way is to show by contradiction that if N = pq then one of p and q must be less than or equal to VN. Thus, when trying to determine if a number is prime, they need only check for prime divisors less than or equal to VN. Show how you would prove this result and help your students see how to use it to show that 143 see how to use it to show that is not prime and that 569 is prime.
Transcribed Image Text:ssible value of N. (7) (C) A student asks what the best way is to show if a number N is prime. What do you say? At first students think one has to try to divide N by all primes less than N and if none divide N evenly, then N is prime. But, a better way is to show by contradiction that if N = pq then one of p and q must be less than or equal to VN. Thus, when trying to determine if a number is prime, they need only check for prime divisors less than or equal to VN. Show how you would prove this result and help your students see how to use it to show that 143 see how to use it to show that is not prime and that 569 is prime.
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