Using Mathematical Induction to Prove 2^(3n) - 3^n is divisible by 5

In this video we can use mathematical induction to prove that

2³ⁿ - 3ⁿ is divisible by 5 ∀ n ≥ 1

1. The first step in mathematical induction is always the basis test which is to see if this condition or expression else true for n = 1. If n = 1, then...
   
   2^3x1 - 3¹ = 8 - 3 = 5
   
   Is 5 divisible by 5? Yes it is, so the expression passes the basis test
    
2. Now because we have found that this statement is true for n = 1, we assume that it holds true when n = k (where k is any positive integer). So we let...
   
   2^3k - 3^k = 5J where J = 1,2,3,...
   
   We can rewrite this expression as
   
   2^3k = 5J + 3^k
   
   and this step will become important later on...
    
3. The next step of mathematical induction is the inductive test. We've assumed that if this statement is true for n = k. But does it hold true for when n = k + 1? So, substituting in n = k + 1, we get...
   
   2^3(k+1) - 3^k+1
   Please watch the video for the full analysis