[Math] Prove by induction that (5^(n))-1 is divisible by 4 for all natural numbers n.

Question

Prove by induction that $5^n-1$ is divisible by $4$ for all natural numbers $n$.

I got $P(k+1)=5^{k+1}-1$ but I don't where to go now.

Answer 1

Note that $5^{k+1}-1=5(5^k-1)+4$. Now use your induction assumption that says $4|5^k-1$.