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 Possible or not? (Posted on 2015-01-17)
Prove or disprove the following:
For any integer number N there exists at least one integer number M, such that the decimal presentation of M*N needs only two distinct digits.

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 re: possible solution | Comment 2 of 6 |
(In reply to possible solution by broll)

I had just come up with the same proof, broll, and was about to write it up.  Thanks for saving me the trouble, broll.

Not sure why you single out N = 0.  Lots of numbers only require 1 digit.  Any number that does not have a factor of 2 or 5 only needs 1 digit.  Also, 2 and 4 and 5 and 6 and 8 times any repunit only needs one digit.

(Of course, if we allow M = 0, then this problem is difficulty 1, and it is true for rational, irrational, transcendental and imaginary values of N)

Edited on January 17, 2015, 9:19 pm
 Posted by Steve Herman on 2015-01-17 21:13:30

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