## Math Reflections

Posted by JB on April 5, 2012 – 7:55 pm

What 5 digit number when multiplied by 54321 produces a 10 digit number end with 12345?

Posted by JB on April 5, 2012 – 7:55 pm

What 5 digit number when multiplied by 54321 produces a 10 digit number end with 12345?

April 5th, 2012 at 8:43 pm

99945

April 8th, 2012 at 4:16 pm

99945

*was beaten by miles*

April 8th, 2012 at 9:22 pm

hi Krazeedude…you got to tell Miles not to treat you like that, no matter how much he wants to know the answer

April 9th, 2012 at 9:13 am

I can’t find a nice (e.g. modulo arithmetic technique). So here’s a direct method.

Let the number be abcde i.e. abcde*54321 = y*10^5 + 12345

We don’t care what y is, so I’ll completely ignore it.

You might find it useful to practice long multiplications to follow this solution.

The method is to determine e, then use that to determine d, etc.

Do a long multiplication