I do not believe it is possible.
X must end in a 2, 4, or 8 for any power of X to end in a 4.
If X ends in 2 or 8, X^n will end in a 4 if n is 2 mod 4. However, if X is 2 or 8, then 2X will always be 0 mod 4, so these won't work.
Similarly, if X ends in 4, X^n will end in a 4 if n is odd. However, if X is 4 then 2X will obviously be even, so this won't work either.

Posted by tomarken
on 20140314 10:01:09 