Diophantine Equation - Exponential Diophantine Equations

Exponential Diophantine Equations

If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation. One example is the Ramanujan–Nagell equation, 2n − 7 = x2. Such equations do not have a general theory; particular cases such as Catalan's conjecture have been tackled. However, the majority are solved via ad hoc methods such as Størmer's theorem or even trial and error.