\section*{Problem 2}

Which is greater: \(31^{11}\) or \(17^{14}\) ? [No calculators allowed!]


\section*{Solution}

\[
17^{2}=289>9.31 \text {. So } 17^{14}>9^{7} 31^{7} \text {. But } 3^{7}=2187>31^{2} \text {. Hence } 17^{14}>31^{11} \text {. }
\]

