On the Diophantine Equation n^x-17^y=z^2
Background and Objectives: to find the non-negative integer solutions of the Diophantine equation , where is a positive integer, which satisfies one of the following conditions: 1. 2. and 3. and . Methodology: to prove by using the basic concepts of number theory. Main Results: If , then the equation has the only non-negative integer solution . If , then the non-negative integer solutions are and , where is a non-negative integer such that is an integer. Moreover, if and , then the equation has the unique non-negative integer solution . Conclusions: Let be a positive integer. If or and , then the equation has the unique solution . If , then the equation has the solutions and , where is a non-negative integer such that is an integer. , number=3 September-December, journal=Burapha Science Journal, author=Tadee, Suton, year=2024, month=Sep., pages=902–909