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\centerline{\bf THEORY OF NUMBERS, Math 115 A}
\centerline{\bf Homework 1 Due Wednesday October 2}
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\begin{enumerate}

\item Use the well-ordering property to show that $\sqrt{3}$ is irrational. 

\item Find a formula for $\sum_{k=1}^n k^3$.

\item Find and prove a simple formula for the sum of the first $n$
Fibonacci numbers with odd indices when $n$ is a positive integers,
i.e. find a formula for $f_1+f_3+\dots+f_{2n-1}$

\item Find the quotient and remainder in the division algorithm, with
divisor 17 and dividend 

a) 100, b) -44, c) 289

\item Show that if $a$ is an integer, then 3 divides $a^3-a$.

\item Show that the $n$-th Fibonacci number $f_n$ is divisible by 4
if and only if $n$ is divisible by 6.

\end{enumerate}

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