is a-b always a factor of a^n-b^n .........if yes prove

TIll we get the solution...Here's something interesting.

we have,

a = b mod (a-b)         

aⁿ = bⁿ mod (a-b)

aⁿ - bⁿ = 0 mod(a-b)

hence (a-b) will always be a factor of (aⁿ - bⁿ ) for every real n .

but here is the best proof given by nishant sir....x=y is always a root of x^n-y^n..so (x-y)(polynomial)....amazing naaa??????????

But see..

a^n - b^n = (a-b)(something ...)

We can apply 'reverse-engineering' here .. cant we ?