In this paper, authors have addressed the Diophantine equation \(x^{7} - y^{7} = 19487171\) , \(x,y \in Z\) , where \(Z\) represents the set of integers, for determining the ordered pairs \(\left( {x,y} \right) \in Z \times Z\) that satisfy this equation. To achieve this goal, authors have considered the well known factorization and modular arithmetic methods. It was shown by the results that the ordered pairs \(\left( {x,y} \right) = \left( {0, - 11} \right),\left( {11, 0} \right) \in Z \times Z\) are the only ordered pairs that satisfies the equation \(x^{7} - y^{7} = 19487171\) .
