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

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anonymous
 3 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
 3 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
 3 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
 3 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
 3 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?
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