Can neural networks be used to study (elementary) number theoretic problems? What are examples where this has been done in the past? Or is there on the contrary an understanding that neural networks are not helpful for such problems?
To make the question more concrete, let me give an example of the kind of number theoretic problem I'm thinking of: given two natural numbers a and b I may want to compute the rounded down quotient int(a/b). Naively I would restrict to 64 bit unsigned numbers and build a neural network that has 128 neurons in the input layer and 64 neurons in the output layer representing the binary expansion of the numbers. Assuming I laid out the network properly and trained it well, would I be expected to get useful output? In particular, would I be able to interpret the output as a number and would it often be the right answer?
Note: the reason why I think of this as problem as "number theoretic" is because I want to compute int(a/b) rather than the rational number a/b. This is essentially a step in Euclid's algorithm. So the non-linear behaviour int(4/3) = 1, int(5/3) = 1, int(6/3) = 2 is crucial and would need to be recognizable in the output.