Use mathematical induction to prove that the assertion is true for $\displaystyle n\ge 1$. $\displaystyle 5^n-1$ is divisible by $\displaystyle 4$.

basis$\displaystyle n_{o}=1$ then $\displaystyle 5^1-1=4$ is divisible by $\displaystyle 4$.

IHlet $\displaystyle 1\le l<k$ and assume $\displaystyle 5^l-1$ is divisible by $\displaystyle 4$.

Induction Step

$\displaystyle 5^{k}-1=(5)5^{k-1}-1$

Since $\displaystyle 5^{k-1}-1$ is divisble by $\displaystyle 4$ (by the induction hypothesis) then $\displaystyle (5)5^{k-1}-1$ is also divisible by $\displaystyle 4$

Is this right?

What is wrong with the latex