Abstract: In number theory, the Diophantine equation is an important branch which has drawn extensive research. In this paper, the
integer solution to the Diophantine equation x2 + 1 024 = y15 is studied by applying the knowledge of algebraic number theory and
congruence theory, and it is acquired that the Diophantine equation x2 + 1 024 = y15 has no integer solution.

Key words: Diophantine equation, integer solution, algebraic number theory, congruence theory