Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1

As is the case with all induction questions, we first need to show that the result is true for the base case, in this case n = 1.If n = 1, we have that the LHS = 6¹ + 4 = 10, which is indeed divisible by 5, so the result holds for n = 1.The next step is to assume the result to be true for some n = k, where k is an integer >= 1. In other words, we assume that6^k + 4 is divisible by 5 for some k.Next we let n = k+1. In this step we show that if it is true for n = k, then the result also holds for n = k+1.If n = k+1, we have that th LHS = 6^k+1 + 4 = 6 * 6^k + 4 = 6*(6^k+ 4) - 20. We know that the first term is divisible by 5 by assumption, since we assumed 6^k + 4 was divisible by 5. We also know that 20 is a multiple of 5, so the RHS can be written as the sum of 2 multiples of 5, which is divisible by 5.So if true for n = k, the result is also true for n = k+1. Hence, by induction, since true for n=1, the result must be true for n = 2, n =3, ... so true for all integers n >= 1.