The Study of the Exponential Diophantine Equation (ퟑퟕ)ퟐ풙+(ퟔ풓+ퟏ)풚=풛

Discussing the solution of the Diophantine equation (37)2𝑥+(6𝑟+1)𝑦=𝑧2, where 𝑟,𝑥,𝑦, and 𝑧 are non-negative integers, is the goal of this study. The authors employed the congruence modulo approach for this. Findings of the study indicate that the Diophantine equation (37)2𝑥+(6𝑟+1)𝑦=𝑧2, where 𝑟,𝑥,𝑦, and 𝑧 are non-negative integers, has no solution in the set of non-negative integers.