Induction: Divisibility Proof example 6 (a^n - b^n is divisible by a - b)

[nahbro]

where did the a^k multiplying by (a-b) go at 4:22?

[vanheedavid]

2 lines before the last one, where is a^k

[justinwu]

Hi Mr Woo! 

I think with this approach, you can also prove that a^n + b^n is divisible by a + b for all odd values of n. 

[amrutamelavanki]

If A is a non-zero integer and b is any integer, then
a/b=a/-b and -a/-b
Please answer this question sir.

[esWhistler]

why must a > b? A negative number can't be a divider?

[amitkumarvijay]

What if n is negative number, will it not divisible?

[krishnarajput]

a & b are either prime or composite

[mrasifspeaks]

Hi sir woo! plz give me the proof of a^n-b^n is divisible by a+b for n is even plz as soon as possible .

[cipherunity]

Another way of proving this

Let f(x) = x^n - b^n Therefore f(b) = b^n - b^n = 0

Hence x - b divides x^n - b^n

Replacing x with a, we get a - b divides a^n - b^n

[prince]

Bro! Its mathematical induction but any other way?

[srishtitomar]

CBSE board ke questions solve karo okoko

[lilian]

obrigado professor, mesmo não sabendo inglês conseguir entender o raciocínio. Abraços.