  The paper introduces a connectionist network approach to find numerical
solutions of Diophantine equations as an attempt to address the famous
Hilbert's tenth problem. The proposed methodology uses a three layer feed
forward neural network with back propagation as sequential learning procedure
to find numerical solutions of a class of Diophantine equations. It uses a
dynamically constructed network architecture where number of nodes in the input
layer is chosen based on the number of variables in the equation. The powers of
the given Diophantine equation are taken as input to the input layer. The
training of the network starts with initial random integral weights. The
weights are updated based on the back propagation of the error values at the
output layer. The optimization of weights is augmented by adding a momentum
factor into the network. The optimized weights of the connection between the
input layer and the hidden layer are taken as numerical solution of the given
Diophantine equation. The procedure is validated using different Diophantine
Equations of different number of variables and different powers.
