Pete chooses 1004 monic quadratic polynomial f1,⋯,f1004, such that each integer from 0 to 2007 is a root of at least one of them. Vasya considers all equations of the form f_{i}\equal{}f_{j}(i\not \equal{}j) and computes their roots; for each such root , Pete has to pay to Vasya 1 ruble . Find the least possible value of Vasya's income. quadraticsalgebrapolynomialgeometrygeometric transformationalgebra proposed