Article
On the diophantine equation $ax^2+b=cy^n$
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Abstract
In this paper, we study the diophantine equation $ax^2+b=cy^n$ where $a, b, c, n, x, y$ are positive integers and we prove some results concerning this equation when $b = 7, 11$. In Theorem 3, we are able to correct the result of Demirpolat and Cenberci appeared in [9].
Keywords
Diophantine equation, perfect square, quadratic field.
Citation
Abu Muriefah, F. S. & Al-Rashed, A. (2013). On the diophantine equation $ax^2+b=cy^n$. Journal of Analysis & Number Theory, 1(1), 15–21.
F. S. Abu Muriefah and A. Al-Rashed, “On the diophantine equation $ax^2+b=cy^n$,” Journal of Analysis & Number Theory, vol. 1, no. 1, pp. 15–21, 2013.
Abu Muriefah FS, Al-Rashed A. On the diophantine equation $ax^2+b=cy^n$. Journal of Analysis & Number Theory. 2013;1(1):15–21.
Abu Muriefah, F. S. and Al-Rashed, A. (2013), ‘On the diophantine equation $ax^2+b=cy^n$’, Journal of Analysis & Number Theory, 1(1), pp. 15–21.
Abu Muriefah, Fadwa S., and Amal Al-Rashed. “On the Diophantine Equation $ax^2+b=cy^n$.” Journal of Analysis & Number Theory, vol. 1, no. 1, 2013, pp. 15–21.
Abu Muriefah, Fadwa S., and Amal Al-Rashed. “On the Diophantine Equation $ax^2+b=cy^n$.” Journal of Analysis & Number Theory 1, no. 1 (2013): 15–21.
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Published by: Engineering Journals
