Abstract
Let p be a prime number ≥ 5, and n a positive integer > 1. This note is concerned with the diophantine equation x4 − y4 = nzp. We prove that, under certain conditions on n, this equation has no non-trivial solution in Z if p ≥ C(n), where C(n) is an effective constant.
Publisher
Cambridge University Press (CUP)
Cited by
9 articles.
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1. On the Difference of Two Fourth Powers;Proceedings of the Edinburgh Mathematical Society;2023-11-10
2. Solutions to $$x^4+py^4=z^4$$ in cubic number fields;Archiv der Mathematik;2022-06-10
3. On the integral solutions of the Diophantine equation x4 + y4 = 2kz3 where k > 1;INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020;2021
4. INTEGERS REPRESENTED BY REVISITED;Bulletin of the Australian Mathematical Society;2020-05-20
5. Generalized Fermat equations: A miscellany;International Journal of Number Theory;2014-11-24