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On the difference of two fourth powers
Published online by Cambridge University Press: 10 November 2023
Abstract
We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p, we find solutions to $p=x^4-y^4$ if $p\equiv 11$ (mod 16) and $p^3=x^4-y^4$ if $p\equiv 3$ (mod 16) in all cubic extensions of $\mathbb{Q}(i)$.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 1 , February 2024 , pp. 142 - 150
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.