Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
JoãoVitorMC
Group Title
Prove that for any integer n, at least one of the integers n, n+2, n+4 is divisible by 3 .
 2 years ago
 2 years ago
JoãoVitorMC Group Title
Prove that for any integer n, at least one of the integers n, n+2, n+4 is divisible by 3 .
 2 years ago
 2 years ago

This Question is Closed

JakeV8 Group TitleBest ResponseYou've already chosen the best response.1
I 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.
 2 years ago

JakeV8 Group TitleBest ResponseYou've already chosen the best response.1
That's not a proof, but maybe you could use that logic to formalize in a proof format.
 2 years ago

JoãoVitorMC Group TitleBest ResponseYou've already chosen the best response.0
ok thks i'll try
 2 years ago

JakeV8 Group TitleBest ResponseYou've already chosen the best response.1
you 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.
 2 years ago

JakeV8 Group TitleBest ResponseYou've already chosen the best response.1
so n + 2 = (m + 1) + 2 = m + 3... and since m is divisible by 3, so is m+3
 2 years ago

JoãoVitorMC Group TitleBest ResponseYou've already chosen the best response.0
is this make sense? n+(n+2)+(n+4) = 3n+6 , but (3n+6)/3 = n+2 is that sufficient proof?
 2 years ago
See more questions >>>
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.