Gent2324
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prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

is that acceptable proof for a level maths? thanks
Last edited by Gent2324; 4 months ago
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mqb2766
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Sounds ok to me.

(Original post by Gent2324)
prove 8n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

is that acceptable proof for a level maths? thanks
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Gent2324
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(Original post by mqb2766)
Sounds ok to me.
wait i wrote it down wrong its actually meant to say prove n^3 + 2 is not divisibly by 8, not 8n^3 +2, would it still be fine to do that proof?
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mqb2766
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Can you edit / reply with the "correct" info?
(Original post by Gent2324)
wait i wrote it down wrong its actually meant to say prove n^3 + 2 is not divisibly by 8, not 8n^3 +2, would it still be fine to do that proof?
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Gent2324
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(Original post by mqb2766)
Can you edit / reply with the "correct" info?
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.

but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
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mqb2766
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How do you get the 8* (x^3) on line 3?
That was ok in the Original version you posted but now it magically appears? I can't see this would be valid as stands.

A tiny bit in front of it could be to show n must be even, hence the Original 8n^3+2 would be an ok statement, hence the Original proof would be ok.


(Original post by Gent2324)
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.

but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
Last edited by mqb2766; 4 months ago
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RDKGames
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(Original post by Gent2324)
prove n^3 + 2 is not divisible by 8.
i used proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

i saw this on reddit as it came up on this years as paper, they said: Suppose 8m^3+2 were divisible by 8, so that it is equal to 8n for some integer n. Then 8m^3+2=8n so that 2=8n-8m^3=8(n-m^3). Which would mean that 2 is divisible by 8.

but i thought the question asked for 8(n^3 +2), turns out theres no 8. so is that proof still acceptable as i kind of added an 8 in from nowhere on the 3rd line
This is still a mess of a post. I'm not even sure what you're asking, but obviously misreading the question would lose you marks, but using the idea of contradiction would give a mark or two.
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mqb2766
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Edited post 6 with a fix at the start.
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Gent2324
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(Original post by RDKGames)
This is still a mess of a post. I'm not even sure what you're asking, but obviously misreading the question would lose you marks, but using the idea of contradiction would give a mark or two.
sorry let me ask it here, ignore all the other posts i made:

prove n^3 + 2 is not divisible by 8.
If n is odd, then n^3+2 is odd, so isn't divisible by 8.

If n is even, then n = 2x where x is an integer. Then n^3 +2 = 8x^3 +2

proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

is that correct proof?
Last edited by Gent2324; 4 months ago
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mqb2766
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Sounds ok now.
(Original post by Gent2324)
sorry let me ask it here, ignore all the other posts i made:

prove n^3 + 2 is not divisible by 8.
If n is odd, then n^3+2 is odd, so isn't divisible by 8.

If n is even, then n = 2x where x is an integer. Then n^3 +2 = 8x^3 +2

proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

is that correct proof?
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RDKGames
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(Original post by Gent2324)
sorry let me ask it here, ignore all the other posts i made:

prove n^3 + 2 is not divisible by 8.

proof by contradiction:
suppose 8x^3 +2 is divisible by 8, therefore 8x^3 +2 = 8n
rearranging, 2 = 8n - 8x^3 = 8(n-x^3), if true, then 2 is divisible by 8, it is impossible for 2 to be divisible by 8(n-x^3) if n and x are integers.

is that correct proof?
Pretty much, though I feel uneasy with you saying "for 2 to be divisible by 8(n-x^3)" when the natural thing to say after "2 is divisible by 8" is "it's impossible for 2 to be divisible by 8" hence the contradiction.

Also, it's slightly awkward when you take their n and use x in its place. You should just say "Suppose 8n^3+2 is div. by 8, then 8n^3 + 2 = 8k for some integer k"
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Gent2324
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(Original post by mqb2766)
Sounds ok now.
ok thank you for help, i found out that the reddit post i was referring to was actually a reply of someone who got to n^3 +2 = 8x^3 +2 hence why it wasnt proof on its own
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