A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Prove that for any integer n, at least one of the integers n, n+2, n+4 is divisible by 3 .
anonymous
 4 years ago
Prove that for any integer n, at least one of the integers n, n+2, n+4 is divisible by 3 .

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I don't recall how to organize a proof of this type. But you might take it one case at a time... If n is divisible by 3, then you're done. If n is not divisible by 3, then it must either be 1 greater or 2 greater than a number that is divisible by 3 (i.e., if it was 3 greater than a number divisible by 3, it would also be divisible by 3). If n is one greater, then n + 2 is three greater than the number divisible by 3, therefore n+2 is also divisible by 3. If n is two greater than a number divisible by 3, then n + 4 will make it 6 greater than that number, making n + 4 divisible by 3.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That's not a proof, but maybe you could use that logic to formalize in a proof format.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you could use another variable to help. If n is not divisible by 3, then if m is divisible by 3, n must be m + 1 or m + 2.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so n + 2 = (m + 1) + 2 = m + 3... and since m is divisible by 3, so is m+3

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is this make sense? n+(n+2)+(n+4) = 3n+6 , but (3n+6)/3 = n+2 is that sufficient proof?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.