A Solution Maple Can’t Do

This problem is from Dr. Ehrke.

In this problem of the week we will try to solve a problem that WolframAlpha, Maple, etc.. can’t even do.  Find all integer solutions to the implicit equation

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An integer solution is a pair (x,y) that makes both sides of the equation equal, but x and y can only be integers.  Hint:  Consider what the last digit of the right and left hand side would be for different inputs (x,y).

Solution

This problem had one correct response from Wyatt Witemeyer.  

See the solution explained in the video below.