SweetCherry1
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I need help on this question...
n is an integer greater than one,
explain why n3-n is divisible by six... the 3 is supposed to be a power btw.
Thanks for the help :P x
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(Original post by SweetCherry1)
I need help on this question...
n is an integer greater than one,
explain why n3-n is divisible by six... the 3 is supposed to be a power btw.
Thanks for the help :P x
What have you tried so far?

From a quick skim, it seems that you could try induction.

Edit - There's a much quicker (and more elegant) way using number theory. Try factorizing and think about the properties of your brackets.
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AdamWats0n
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3n - n is not always divisible by 6. For example, 3(2) - 2 = 4 which is not divisible by 6.

If you mean n^3 that has to be proved by induction which is way beyond GCSE. Try the Maths forums go google it.
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(Original post by AdamWats0n)
3n - n is not always divisible by 6. For example, 3(2) - 2 = 4 which is not divisible by 6.

If you mean n^3 that has to be proved by induction which is way beyond GCSE. Try the Maths forums go google it.
It doesn't need induction, I thought this as well but you can do it by factorizing.
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AdamWats0n
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(Original post by Arithmeticae)
It doesn't need induction, I thought this as well but you can do it by factorizing.
Yeah, just looking into that now.
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SweetCherry1
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(Original post by AdamWats0n)
3n - n is not always divisible by 6. For example, 3(2) - 2 = 4 which is not divisible by 6.

If you mean n^3 that has to be proved by induction which is way beyond GCSE. Try the Maths forums go google it.
yeah it is n^3- I didn't know what ^ meant.Lol :P Anyway Im doing further maths GCSE and its in the past paper which I cant get the answers to- so there must be an easier way...
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(Original post by SweetCherry1)
yeah it is n^3- I didn't know what ^ meant.Lol :P Anyway Im doing further maths GCSE and its in the past paper which I cant get the answers to- so there must be an easier way...
First off, we can see that n^3-n = n(n^2-1) = (n-1)n(n+1)

What do you notice about these numbers?
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SweetCherry1
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(Original post by Arithmeticae)
First off, we can see that n^3-n = n(n^2-1) = (n-1)n(n+1)

What do you notice about these numbers?
nothing- what do you notice?
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AdamWats0n
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(Original post by Arithmeticae)
First off, we can see that n^3-n = n(n^2-1) = (n-1)n(n+1)

What do you notice about these numbers?
Beat me too it again! Yeah, this way is so much quicker, though I would check that your teacher didn't want induction because this might not be possible for every case.
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AdamWats0n
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(Original post by SweetCherry1)
nothing- what do you notice?
Consecutive numbers!
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(Original post by SweetCherry1)
nothing- what do you notice?
They're consecutive.

(Original post by AdamWats0n)
Beat me too it again! Yeah, this way is so much quicker, though I would check that your teacher didn't want induction because this might not be possible for every case.
It is possible for every case in the natural numbers, unless you were talking about something else (that is, if you count 0 as a multiple of 6, which I guess is technically true as 0 is a multiple of everything O_o)
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AdamWats0n
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(Original post by Arithmeticae)
They're consecutive.



It is possible for every case in the natural numbers, unless you were talking about something else (that is, if you count 0 as a multiple of 6, which I guess is technically true as 0 is a multiple of everything O_o)
Yeah, I was unsure if they were meant to no proof by induction for the course but I don't think so now. Lets not get into maths arguments about 0, that go rage for quit a while!
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SweetCherry1
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(Original post by AdamWats0n)
Consecutive numbers!
:eek: so what?- how does it show its a multiple of six . Am I supposed to know that 3 consecutive no.s are multiples of six??
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AdamWats0n
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(Original post by SweetCherry1)
:eek: so what?- how does it show its a multiple of six . Am I supposed to know that 3 consecutive no.s are multiples of six??
Of any three consecutive numbers, one will be a multiple of 2 and one a multiple of 3. That means the product of the numbers is divisible by 6. Hope you've got it because I've got to go now!
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iPads Anonymous
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The answer is 3


Posted from TSR Mobile
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SweetCherry1
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(Original post by AdamWats0n)
Of any three consecutive numbers, one will be a multiple of 2 and one a multiple of 3. That means the product of the numbers is divisible by 6. Hope you've got it because I've got to go now!
cool thanks!
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