Solution of the Exponential Diophantine Equation 10𝒙 −𝟐𝟗𝒚 = 𝒛𝟐

Abstract

The Diophantine equation 10^𝑥 − 29^𝑦 = 𝑧², where 𝑥,𝑦,𝑧 are non negative integers, has been examined by the author of this paper. By applying modular arithmetic method and Catalan’s Conjecture, we showed that (𝑥,𝑦,𝑧) = (0,0,0) and (1,0,3) are two non-negative integer solutions of this Diophantine equation.