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anonymous
 one year ago
mathematical induction to prove that n 3 − n is divisible by 3, for every positive integer n
anonymous
 one year ago
mathematical induction to prove that n 3 − n is divisible by 3, for every positive integer n

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(n^3n=n(n^21)=n(n1)(n+1)\) that should help.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1No further questions?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not yet... im working it thru

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok this is where im at P(x+1)=(x+1)((x+1)−1)((x+1)+1) = 3m do i divide

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you don't need anything, except for a little logic.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1here, tell me what happens if you have a product that consists of integers and one of these integers are divisible by 3? Do you agree that the result is divisible by 3?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, lets come back to the fact that you want to prove that: *n(n1)(n+1)* is divislbe by 3, \(\forall {\bf n \in \mathbb Z}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, lets consider 3 possible cases (for possible integer k) 3k, 3k+1, and 3k+2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If your number n falls under the category 3k (Such that n > 3k) then the *n* component of *n(n1)(n+1)*, is divisible by 3, and thus the entire product *n(n1)(n+1)* is divislbe by 3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If your number n falls under the category 3k+1 (Such that n > 3k+1) then the *n1* component of *n(n1)(n+1)*, is divisible by 3, and thus the entire product *n(n1)(n+1)* is divislbe by 3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And then if: n > 3k+2 then the *n+1* makes it divisible by 3.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Do I sound rediculous, or is it understandable.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no u dont.. im just trying to absorb the concept

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my brain is a bit mathed out

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\displaystyle\int\)\(\theta\) \(f(u)+nn=y\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If you have more questions to ask, I wil be back if I am online.
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