Steepest Ascent Hill Climbing For A Mathematical Problem
  The paper proposes artificial intelligence technique called hill climbing to
find numerical solutions of Diophantine Equations. Such equations are important
as they have many applications in fields like public key cryptography, integer
factorization, algebraic curves, projective curves and data dependency in super
computers. Importantly, it has been proved that there is no general method to
find solutions of such equations. This paper is an attempt to find numerical
solutions of Diophantine equations using steepest ascent version of Hill
Climbing. The method, which uses tree representation to depict possible
solutions of Diophantine equations, adopts a novel methodology to generate
successors. The heuristic function used help to make the process of finding
solution as a minimization process. The work illustrates the effectiveness of
the proposed methodology using a class of Diophantine equations given by a1. x1
p1 + a2. x2 p2 + ...... + an . xn pn = N where ai and N are integers. The
experimental results validate that the procedure proposed is successful in
finding solutions of Diophantine Equations with sufficiently large powers and
large number of variables.
