Is there any mathematical operation on Integers that yields the same result as doing bitwise "AND"? I'll provide a little bit of a background so you guys can better understand my question:
Let's say I have two positive, non-zero Binary Numbers.(Which can, obviously, be mapped to integers)
I will then proceed onto doing an "AND" operation for each bit, (I think that's called a bitwise operation) which will yield yet another binary number.
Ok. Now this new Binary number can, in turn, also be mapped to an Integer.

My question is: Is there any Integer operation I can do on the mapped Integer values of the two original binary numbers that would yield the same result?

Thanks in advance.
EDIT       : I forgot to mention that What I'm looking for is a mathematical expression using things like +,-,/,pow(base,exp) and the like. I'm not 100% sure (I'm a compuer scientist) but I think what I'm looking for is an isomorphism.
LAST EDIT: I think this will clear any doubts as to what sort of mathematical expression I'm looking for. I wanted something like:
The bitwise AND of two Integers A and B is always equal to (AB)X(B)X(3).

The general feeling I got is that it's not possible or extremely difficult to prove(either its validity or non-validity)

If you have a bound on the size of the integers involved then you can find some polynomial whose values equal bitwise AND using Lagrange interpolation.
