# Prove that the numbers q and r are unique

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Q: http://prntscr.com/vkjz31

If q and r where both 0 then a = (0 x 0) + 0 where b = 0

This is a contradiction as b > 0.

Is that good enough or do I need show a contradiction for every instance where q = r?

If q and r where both 0 then a = (0 x 0) + 0 where b = 0

This is a contradiction as b > 0.

Is that good enough or do I need show a contradiction for every instance where q = r?

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#2

(Original post by

Q: http://prntscr.com/vkjz31

If q and r where both 0 then a = (0 x 0) + 0 where b = 0

This is a contradiction as b > 0.

Is that good enough or do I need show a contradiction for every instance where q = r?

**TSR360**)Q: http://prntscr.com/vkjz31

If q and r where both 0 then a = (0 x 0) + 0 where b = 0

This is a contradiction as b > 0.

Is that good enough or do I need show a contradiction for every instance where q = r?

You need every instance.

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#3

**TSR360**)

Q: http://prntscr.com/vkjz31

If q and r where both 0 then a = (0 x 0) + 0 where b = 0

This is a contradiction as b > 0.

Is that good enough or do I need show a contradiction for every instance where q = r?

It also fails as you then assume b=0 and say this contradicts b>0. Well don't assume b=0 then - it's not a valid value.

I would suggest looking up the proof and fully understanding the logic of it, otherwise this thread is likely to run for a very long time.

PS: I am somewhat surprised this is A-level. The logic involved is only solidly taught in first year uni.

Last edited by ghostwalker; 9 months ago

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I'm assuming q1 means q1 has the same properties as q but they're not identical.

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(Original post by

If q=r=0, then a=0, so you're attempting to show that zero can be written uniquely in the form bq+r. With this method you'll then need to do 1, 2, ..., and possibly the negative integers depending on what values a can take.

It also fails as you then assume b=0 and say this contradicts b>0. Well don't assume b=0 then - it's not a valid value.

I would suggest looking up the proof and fully understanding the logic of it, otherwise this thread is likely to run for a very long time.

PS: I am somewhat surprised this is A-level. The logic involved is only solidly taught in first year uni.

**ghostwalker**)If q=r=0, then a=0, so you're attempting to show that zero can be written uniquely in the form bq+r. With this method you'll then need to do 1, 2, ..., and possibly the negative integers depending on what values a can take.

It also fails as you then assume b=0 and say this contradicts b>0. Well don't assume b=0 then - it's not a valid value.

I would suggest looking up the proof and fully understanding the logic of it, otherwise this thread is likely to run for a very long time.

PS: I am somewhat surprised this is A-level. The logic involved is only solidly taught in first year uni.

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#6

(Original post by

There's questions a lot harder than this in my A level textboook. I'm using a beginner number theory textbook to help me understand the proofs more thoroughly, so there might be some overlap between a-level and uni maths but I don't see any other way of being able to do the proofs in a-level as it just isn't very logical.

**TSR360**)There's questions a lot harder than this in my A level textboook. I'm using a beginner number theory textbook to help me understand the proofs more thoroughly, so there might be some overlap between a-level and uni maths but I don't see any other way of being able to do the proofs in a-level as it just isn't very logical.

Can you give an example of an A level proof that you think is "more difficult" than this?

Last edited by davros; 9 months ago

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#7

**TSR360**)

There's questions a lot harder than this in my A level textboook. I'm using a beginner number theory textbook to help me understand the proofs more thoroughly, so there might be some overlap between a-level and uni maths but I don't see any other way of being able to do the proofs in a-level as it just isn't very logical.

Last edited by ghostwalker; 9 months ago

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#8

**TSR360**)

There's questions a lot harder than this in my A level textboook. I'm using a beginner number theory textbook to help me understand the proofs more thoroughly, so there might be some overlap between a-level and uni maths but I don't see any other way of being able to do the proofs in a-level as it just isn't very logical.

As far as this actual proof goes, you don't seem to understand what you're actually trying to prove. A proof of this would normally begin something like:

"Suppose that and , with and . Then ..."

(or alternatively, instead of "Then..." you might have "Suppose (for contradiction) that...").

You don't even mention and , and instead talk about "if q and r are identical", which doesn't really make any sense at all. I

**think**you're trying to talk about two representations

and

where the q, r in the 2nd representation are different from in the 1st representation. If so, all I can say is that using the same letter to mean two different things is going to be a fast track to madness, here.

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