Is there is any relation between numbers' bits when one is divisible by another? What is the relation between the bits of 36 and the bit sequences of 9 or 4 or 12, or between 10 (1010) and 5 (101), or 21 (10101) and 7 (00111)?
Thanks. I am sorry if some sentence is not correct, but I hope you understand what I want.
Let's take the example of 36.
36 = 0010 0100
36 is 4 * 9, that is
4 = 0100
9 = 1001
If you multiply them (like you would on a normal multiplication) you'll have
0100 x
1001
--------
0100
0000
0000
0100
-------
0100100
So essentially 0100 x 1001 = 0010 0100 (you can repeat the same for any other pair of divisors of course)
Now, is there any special relation that will allow you to get all the divisors of 36 just by looking at its bits? The answer, alas, is no :)
EDIT: there is no KNOWN relation at least but, who knows, in the future maybe some smart mathematician will find one. As of today, the answer is still no.