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Last Digit II (Posted on 2014-03-14) Difficulty: 2 of 5
Can the last digit in the base ten expansion of X2X be 4, whenever X is a positive integer?

If so, give an example. If not, prove it.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution Solution | Comment 1 of 2

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 2014-03-14 10:01:09
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