anonymous
  • anonymous
mathematical induction to prove that n 3 − n is divisible by 3, for every positive integer n
Discrete Math
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • SolomonZelman
\(n^3-n=n(n^2-1)=n(n-1)(n+1)\) that should help.
anonymous
  • anonymous
thank you
SolomonZelman
  • SolomonZelman
No further questions?

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anonymous
  • anonymous
not yet... im working it thru
anonymous
  • anonymous
ok this is where im at P(x+1)=(x+1)((x+1)−1)((x+1)+1) = 3m do i divide
SolomonZelman
  • SolomonZelman
you don't need anything, except for a little logic.
SolomonZelman
  • SolomonZelman
here, 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?
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
Ok, good.
SolomonZelman
  • SolomonZelman
Now, lets come back to the fact that you want to prove that: *n(n-1)(n+1)* is divislbe by 3, \(\forall {\bf n \in \mathbb Z}\)
SolomonZelman
  • SolomonZelman
Ok, lets consider 3 possible cases (for possible integer k) 3k, 3k+1, and 3k+2
SolomonZelman
  • SolomonZelman
If your number n falls under the category 3k (Such that n --> 3k) then the *n* component of *n(n-1)(n+1)*, is divisible by 3, and thus the entire product *n(n-1)(n+1)* is divislbe by 3.
SolomonZelman
  • SolomonZelman
If your number n falls under the category 3k+1 (Such that n --> 3k+1) then the *n-1* component of *n(n-1)(n+1)*, is divisible by 3, and thus the entire product *n(n-1)(n+1)* is divislbe by 3.
SolomonZelman
  • SolomonZelman
And then if: n --> 3k+2 then the *n+1* makes it divisible by 3.
SolomonZelman
  • SolomonZelman
Do I sound rediculous, or is it understandable.
anonymous
  • anonymous
no u dont.. im just trying to absorb the concept
anonymous
  • anonymous
my brain is a bit mathed out
SolomonZelman
  • SolomonZelman
\(\displaystyle\int\)\(\theta\) \(f(u)+nn=y\)
SolomonZelman
  • SolomonZelman
If you have more questions to ask, I wil be back if I am online.
anonymous
  • anonymous
thank you

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