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\section{Problem 4}   \begin{itemize}   \item   $2^{902} mod 7$   The stategy here is to look for a pattern for mod 7.     $2^0 = 1 mod 7$     $2^1 = 2 mod 7$     $2^2 = 4 mod 7$     $2^3 = 1 mod 7$     $2^4 = 2 mod 7$     $2^5 = 4 mod 7$     $2^6 = 1 mod 7$     $2^7 = 2 mod 7$     $2^8 = 4 mod 7$     ...     $2^900 = 1 mod 7$     $2^901 = 2 mod 7$     {\bf$2^902 = 4 mod 7$}   \end{itemize}