I was looking around for another computational challenge and remembered there was still one left from Feb 2007 in some email correspondence I had with Robert G. Wilson (Bob).
Find a solution to 13^k (mod k) = 36
Background:
Bob was collecting solutions b^k (mod k) and updating the OEIS (Online Encyclopedia of Integer Sequences). He sent an email to me, Alexander Adamchuk, David Wilson, Don Reble, Max Alekseyev, Ryan Propper, and Neil Sloane asking about finding some missing values.
Max and I quickly found values to all the equations except the above one. Max and Ryan followed up with searches to verify least solutions on some of them.
Reference:
http://www.research.att.com/~njas/sequences/A127821
I'm continuing a search for this with one of my machines. I'll make a version of the program I wrote for this (VC++/GMP) available for download soon as well.
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