Diophantine equations
An interesting line of study emerges, however, when we take the opposite tack and insist that not only the coefficients of our equations but their solutions have also to be integers. Here is a classic example.
A box contains spiders and beetles and46legs. How many of each kind of creature are there? This little number puzzle can be solved easily by trial, but it is instructive to note that first, it can be represented by an equation:6b+8s=46, and second that we are only interested in certain kinds of solutions to that equation,namely those where the number of beetles(b)and spiders(s)are counting numbers. In general, a system of equations is called Diophantine when we are restricting our solution search to special number types, typically integer or rational answers are what we are after.