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Age 14 to 16 Short
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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.

You can find more short problems, arranged by curriculum topic, in our short problems collection.