n our attempt to look at one of the challenging problem of modern mathematics we ended up exploring a lot of different areas. Although a lot is known about quadratic residues and non residues it is still surprisingly difficult to generate a non residue deterministically. Here we explore a parallel problem of root finding and analyse various algorithms for the same. The Problem is also related to the problem ofgenerating irreducible polynomials. It is a very exciting problem for even though thetask of finding a non residue is not very difficult we would like a deterministic way to find it.
This report is submitted towards partial fulfillment of the requirements for the award of the Bachelor of Technology (B.Tech) degreein Computer Science and Engineering at the Indian Institute of Technology Goa.