On the existence of solutions of diagonal quartic equation ax^4+by^4=c over finite field

doi:10.19907/j.0490-6756.2022.011001

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On the existence of solutions of diagonal quartic equation ax^4+by^4=c over finite field
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                        10.19907/j.0490-6756.2022.011001
                    
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Clc Number:O156.2
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We prove that when q is not equal to 5,9,13,17,25, and 29, there always exist solutions for the diagonal quartic equation ax^4+by^4=c over F_q.

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Cite this article as: HUANG Bao-Sheng, WU Rong-Jun, TAN Qian-Rong, ZHU Guang-Yan. On the existence of solutions of diagonal quartic equation ax^4+by^4=c over finite field [J]. J Sichuan Univ: Nat Sci Ed, 2022, 59: 011001.

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Received:May 07,2021
Revised:May 16,2021
Adopted:May 21,2021
Online: January 17,2022
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