Question

8power n-3power n is divisible by

Answer 1

Answer:

Prove by Induction that for all n≥1 we have

8n−3nis divisible by 5...(∗)

My proof so far

Step 1: For n=1 we have 81−31=8−3=5 which is divisible by 5.

Step 2: Suppose (*) is true for some n=k≥1 that is 8k−3k is divisible by 5.

Step 3: Prove that (*) is true for n=k+1, that is 8k+1−3k+1 is divisible by 5. We have

8k+1−3k+1=8∗8k−3∗3k

hope this is helpful