Question

if n is a natural number, then 8^n - 3^n is always divisible by____

Answer 1

8^1 -3^1 is divisible by five
8^2 - 3^2 is also divisible by five
so the answer is five

Answer 2

8ⁿ - 3ⁿ where n is natural number ,

if n = 1 => 8¹ - 3¹ = 5 divisible by 5
if n = 2 => 8² -3² =55 , divisible by 5 & 11
if n = 3 => 8³ -3³ = 485 divisible by 5
...................
here we see the result is must be divisble by 5

hence, 8ⁿ -3ⁿ is divisible by 5