Stage: 5 Challenge Level: 
We wonder who can find and explain the shortest and neatest proof that
$5^{2n+1} + 11^{2n+1} + 17^{2n+1}$
is divisible by 33 for every non negative integer n .
Divisibility. Fibonacci sequence. Modulus arithmetic. engineering. Forces. Factors and multiples. Mathematical induction. Short problems. physics. Index notation/Indices.
Published October 1998.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk