Copyright © University of Cambridge. All rights reserved.
Given that $5^j + 6^k + 7^l + 11^m = 2006$ where $j$, $k$, $l$ and $m$ are different non-negative integers, what is the value of $j+k+l+m$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.