Question

If a and b are distinct Integers, prove that a – b is a factor of aⁿ – bⁿ, whenever n is a positive integer. [Hint: write aⁿ = (a – b + b)ⁿ and expand]

Answer 1

a = a - b + b

So, 

= (a – b)[aⁿ integer] 

⇒ aⁿ – bⁿ is divisible by (a – b)