  A recursive algorithm is constructed which finds all solutions to a class of
Diophantine equations connected to the problem of determining ordered n-tuples
of positive integers satisfying the property that their sum is equal to their
product. An examination of the use of Binary Search Trees in implementing the
algorithm into a working program is given. In addition an application of the
algorithm for searching possible extra exceptional values of the
equal-sum-product problem is explored after demonstrating a link between these
numbers and the Sophie Germain primes.
