Prove, that $3^n+3$ can't be a square

Question

How can I prove, that $3^n+3$ can't be a square over the positive integers? The only hint/requirement I have is that I need to solve it using mathematical induction. Any ideas?

Answer 1

Hint $3|3^n+3$.

If $3$ divides a perfect square, then $9$ divides it too.

Answer 2

Because $3^n+3=3(3^{n-1}+1)$ is divided by $3$ and it's not divided by $9$.

Answer 3

For positive integers:

$$3^n+3=3(3^{n-1}+1)$$

But $\;3^n+1\;$ is never divisible by three , so the above has only one prime divisor $\;3\;$ , and this means that can't be a square.