Let [x] be the smallest integer less than or equal to x, and let {x} be the decimal part of x, ie {x}=x-[x]. For any integer n>1, evaluate the following integral from 1 to n, in terms of n:
Given that a and b are non-negative integers and f(x,y)=(x+y-a)(x+y-b), then if f(x,y)=0 has n distinct non-negative integer solutions for (x,y), find how many different polynomials f(x,y) can take.
Note: For example, (1,0) and (0,1) are not distinct solutions.
