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vera_ewing
 one year ago
How do you solve this?
vera_ewing
 one year ago
How do you solve this?

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vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true? I. N is not a prime number. II. N is divisible by pq. III. N is an odd integer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what a prime number is?

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0A number that can only be divided by 1 and itself.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes so what do you think the answer is

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0Well if the prime numbers p and q were 2 and 3, respectively, then that means I. would be incorrect right?

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0Because then N would be 18, which is not a prime number.

vera_ewing
 one year ago
Best ResponseYou've already chosen the best response.0Ohh wait so I. would be correct! Right? @freckles

freckles
 one year ago
Best ResponseYou've already chosen the best response.1would there be any other options though ? for example if p and q are 2 and 3 respectively then you could say one possibly for N is 2(3)=6 doesn't 2(3) go into N=6? Also don't you mean I would be correct?

Here_to_Help15
 one year ago
Best ResponseYou've already chosen the best response.4First, recall that a prime number is only divisible by itself and 1, and that 1 is not a prime number. So, statement I must be true, since a number that can be divided by two prime numbers can’t itself be prime. Next, recall that every number can be written as a product of a particular bunch of prime numbers. Let’s say that N is divisible by 3 and 5. Then, N is equal to 3 ·5 ·p1 ·p2 · · ·, where p1, p2, etc. are some other primes. So, N is divisible by 3 · 5 = 15. Statement II must be true. Finally, remember that 2 is a prime number. So, N could be 6, since 6 = 2 · 3. Statement III isn’t always true.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Awesome explanation by @Here_to_Help15 :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1if N is divisible by two different prime numbers p and q then \(\large \color{black}{\begin{align} N\leq p\times q, \ \{p,q\} \in \mathbb{P} \hspace{1.5em}\\~\\ \end{align}}\) so N cannot be a prime number

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0@Here_to_Help15 Great explanation, just modify it this way (add the capitalized words): "Next, recall that every NONPRIME number can be written as a product"
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