The formal solutions of Diophantine equation agy = bx + c

Abstract

We develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem. Our method not only reveals the internal structure of the equation's solution and yields a numerical algorithm to solve it systematically, but also provides an alternative approach to the discrete logarithm problem.

Keywords

• Number theory
• Diophantine equation
• Congruence
• Discrete logarithm