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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

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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#2

Sounds ok to me.

(Original post by

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

**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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(Original post by

Sounds ok to me.

**mqb2766**)Sounds ok to me.

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#4

Can you edit / reply with the "correct" info?

(Original post by

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?

**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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(Original post by

Can you edit / reply with the "correct" info?

**mqb2766**)Can you edit / reply with the "correct" info?

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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#6

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.

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

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

**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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#7

**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

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(Original post by

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.

**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.

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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#10

Sounds ok now.

(Original post by

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?

**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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#11

(Original post by

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?

**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?

**(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 and use in its place. You should just say "Suppose is div. by 8, then for some integer "

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(Original post by

Sounds ok now.

**mqb2766**)Sounds ok now.

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