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

Abstract

The Diophantine equation 10^𑥠− 29^𑦠= 𑧲, where ð‘¥,ð‘¦,𑧠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 (ð‘¥,ð‘¦,ð‘§) = (0,0,0) and (1,0,3) are two non-negative integer solutions of this Diophantine equation.