Question 12(d)

Question 12(d)

Use mathematical induction to prove that $2^{3n} + 13$ is divisible by $7$ for all integers $n \geq 1$.

Solution

We prove the base case for $n=1$ by substitution, then use the fact that $2^{3n}+13 = 7p$ for some integer $p$ to prove that $2^{3(n+1)}+13 = 7q$ for some other intger $q$.

...

Log in or sign up to see more