On the incompatibility of diophantine equations arising from the Strong Factorial Conjecture

In the present article, we establish new evidence in support of the Strong Factorial Conjecture of Edo and van den Essen [2] by proving it in several special cases. For example, we show that the conjecture holds for powers of linear forms and sums of prime powers of the variables. Finally, we show one way of constructing new examples of polynomials satisfying the conjecture using known examples.