On the Solution of Diophantine Equation (𝟑𝟕)𝟐𝒙+(𝟏𝟐𝓾+𝟏)𝒚=𝒛𝟐

The aim of this study is to discuss the solution of the Diophantine equation (37)2𝑥+(12𝓊+1)𝑦=𝑧2, where 𝓊,𝑥,𝑦, and 𝑧 are non-negative integers. For this, authors have used congruence modulo method. Results of this study indicate that the Diophantine equation (37)2𝑥+(12𝓊+1)𝑦=𝑧2, where 𝓊,𝑥,𝑦, and 𝑧 are non-negative integers, has no solution in the set of non-negative integers.