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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 Answer Comment 2 of 2 |
If X is odd, then X^2X is odd and cannot end in 4. If X ends in 0, then X^2X ends in 0. Suppose X ends in 2, 4, 6, or 8. Since X is even, X=2Y for some integer Y. Then, X^2X=X^4Y=(X^4)^Y. Since X ends in 2, 4, 6, or 8, X^4 ends in 6. Since every power of a number ending in 6 ends in 6, X^2X=(X^4)^Y ends in 6. Therefore, X^2X can never end in 4.

  Posted by Math Man on 2014-03-19 21:04:12
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