Application of high-order hopfield neural networks to the solution of diophantine equations

Hopfield and Tank network with high-order weights is applied to the solution of algebraic problems. Particularly, to the search of positive integer solution of a diophantine equation. The chosen representation avoids using all the possible connections among neurons, so reducing one of the most serious problems of high order: combinatorial growing of connections. The energy function is found to be polynomial of order 2n-1 where n is the order of the equation. Although each network is problem-specific, the building process may be extended to other similar problems without any difficulty.