deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 82f6238..e4514bb 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
= 30a + 5 \\  = 5( 6a + 1) \\  which is clearly divisible by 5.  33)\\  Prove that $n! > 2n$ for all $n \geq 4$.  \paragraph{Solution} Let $P(n)$ be the proposition that $n! > 2^{n}$ for all n $\geq$ 4  \item[+] Basis Step: $P(4)$ is true, because $4! > 2^{4}$  \item[+] Inductive Step: \\  Assume that $k! > 2^{k}$ for all $k\geq4$ \\  Then:  \begin{center}  $(k+1)!$ = $k!(k+1)$ $>$ $2^{k}(k+1)$ $>$ $2^{k}(1+1)$ = $2^{k}2$ = $2^{k+1}$  \end{center}  shows that P(k + 1) is true under the assumption that P(k) is true.\\  34)\\  When $n = 0$ we have that $F_3.0 = F_0 = 0$ which is even.\\  Suppose that $F_3n$ is even for some $n >= 1$. With $n + 1$ we have :\\