Wahyu Risdhyan Ari Wicaksono, I. Made Sulandra, Sisworo
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).
Universitas Negeri Malang Jalan Semarang No. 5, Jawa Timur, Kota Malang, 65145, Indonesia
