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The paper introduces a connectionist network approach to find numericalsolutions of Diophantine equations as an attempt to address the famousHilbert's tenth problem. The proposed methodology uses a three layer feedforward neural network with back propagation as sequential learning procedureto find numerical solutions of a class of Diophantine equations. It uses adynamically constructed network architecture where number of nodes in the inputlayer is chosen based on the number of variables in the equation. The powers ofthe given Diophantine equation are taken as input to the input layer. Thetraining of the network starts with initial random integral weights. Theweights are updated based on the back propagation of the error values at theoutput layer. The optimization of weights is augmented by adding a momentumfactor into the network. The optimized weights of the connection between theinput layer and the hidden layer are taken as numerical solution of the givenDiophantine equation. The procedure is validated using different DiophantineEquations of different number of variables and different powers.

A Connectionist Network Approach to Find Numerical Solutions of Diophantine Equations