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## #1 2006-09-29 22:35:08

ganesh
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### I need a mathematical proof

Hi
Cany anyone of you, using mathematical induction or otherwise, give a flawless proof of (a^n-b^n) always being divisble by (a-b), if the statement is true?
I shall be glad even if someone gives a counter-proof.

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## #2 2006-09-29 22:50:28

mathsyperson
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### Re: I need a mathematical proof

Are there any restrictions on what a, b and n can be?

Presumably a ≠b, but do they all have to be integers as well, or all rationals, or something?

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## #3 2006-10-07 00:48:35

ganesh
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### Re: I need a mathematical proof

The only condition is a,b belong to Natural numbers.
Thanks mathsyperson.

Character is who you are when no one is looking.

## #4 2006-10-07 05:33:11

espeon
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### Re: I need a mathematical proof

hmm if a=2 and b=3 and n=2 then 4-9=-5 which isnt divisible by a-b=-1 and aaaaaaaaaaaaaaaaaaaaaa im getting confused! *Gets dizzy* it would of worked if i knew if -5 was divisible by -1 lol

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## #5 2006-10-07 05:57:59

Ricky
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### Re: I need a mathematical proof

Should be a simple proof by induction.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #6 2006-10-07 17:10:44

George,Y
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### Re: I need a mathematical proof

Yes, but that doesn't need to be an induction.

will do

X'(y-Xβ)=0

## #7 2006-10-07 17:12:24

George,Y
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### Re: I need a mathematical proof

for instance,
a(aa+ab+bb)-b(aa+ab+bb)= (a-b)(aa+ab+bb)= a^3-b^3

X'(y-Xβ)=0

## #8 2006-10-07 18:05:19

ganesh
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### Re: I need a mathematical proof

Thanks George and Ricky, I shall study the proof you have given.

Character is who you are when no one is looking.

## #9 2006-10-08 03:58:51

Ricky
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### Re: I need a mathematical proof

for instance,
a(aa+ab+bb)-b(aa+ab+bb)= (a-b)(aa+ab+bb)= a^3-b^3

You know better than anyone George that an instance does not make a proof.

I'm not sure how you would algebraically solve your formula, would you mind showing me the steps?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #10 2006-10-08 15:15:23

ganesh
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### Re: I need a mathematical proof

I am looking forward to a clear proof by mathematical induction, a flawless elegant proof. Ricky, George and mathsyperon, help me. Help from any other source is most welcome.

Character is who you are when no one is looking.

## #11 2006-10-09 15:35:17

George,Y
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### Re: I need a mathematical proof

#### Ricky wrote:

for instance,
a(aa+ab+bb)-b(aa+ab+bb)= (a-b)(aa+ab+bb)= a^3-b^3

You know better than anyone George that an instance does not make a proof.

I'm not sure how you would algebraically solve your formula, would you mind showing me the steps?

Sure, I shall illustrate Post #6 in detail.

Typically, we wanna know if an-bn could be expressed as (a-b)A, where A is some polynomial.

A could be find out-

Hence

and

Using notation, the proof would be:

Hence

t and k are indexes representing integars, so we can equate them when we do the following algebra.

X'(y-Xβ)=0