On integer solution of the quartic equations over certain fields Z n

Wahyu Risdhyan Ari Wicaksono; I. Made Sulandra; Sisworo

doi:10.1063/5.0125790

← Back to search

On integer solution of the quartic equations over certain fields Z n

Closed

Wahyu Risdhyan Ari Wicaksono, I. Made Sulandra, Sisworo

2023 AIP Conference Proceedings Vol. 2614 Conference paper Cited by 0 SDG 4

Abstract

The integer solution of a cubic equation over certain fields Zn can be determined by using the index function. Based on the idea, we apply the index function to find the integer solution of a quartic equation. Firstly, we identify Euler's Phi-Function theory which is associated with the solution of the quartic equation over the field Zn integer modulo n. Then we identify the primitive roots theory associated with the solution of the quartic equation over Zn. Finally, we identify the index function to find the solution of the given quartic equation. So, we find the condition of the quartic equation ax4 + bx3 + cx2 + dx + e = 0 so that it has an integer solution over Zn, i.e. where n 2b3-8bc+16a2d16a3, with a,b,c,d,e I Z and a 0, and also find what is the solution by using Index Function. © 2023 Author(s).

Affiliations

Universitas Negeri Malang Jalan Semarang No. 5, Jawa Timur, Kota Malang, 65145, Indonesia

View full text (DOI) →

Research at a Glance

Research at a Glance

Topics & SDG Alignment

Collaboration

Author Profile (Selected)

References Overview

Journal & Source

Metadata & Integrity