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JoãoVitorMC
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Prove that for any integer n, at least one of the integers n, n+2, n+4 is divisible by 3 .
 one year ago
 one year 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 .
 one year ago
 one year ago

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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.
 one year 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.
 one year ago

JoãoVitorMC Group TitleBest ResponseYou've already chosen the best response.0
ok thks i'll try
 one year 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.
 one year 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
 one year 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?
 one year ago
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