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.

(In reply to re: possible solution by Steve Herman)

Thanks for that, Steve.

I assumed that 'only two distinct digits' meant exactly two for the very reason you mentioned, i.e. that if one digit is allowed then M=0 works for all N.

But if exactly two digits are required, then N=0 becomes an exception, which is why I noted it.

Posted by broll on 2015-01-17 23:01:42