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PUZZLET 197

Sums of Powers in Alternate Number Bases

Here is a well-known problem that has been around for a while:  a^1 + b^2 + c^3 + d^4 = abcd.

There are several solutions to this in denary, such as: a = 2, b = 4, c = 2, d = 7.

Find all solutions in the number bases less than 10.


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Last Updated: January 17th, 2010.