A Proof of the Lucas-Lehmer Test and its Variations by Using a Singular Cubic Curve
JOURNAL OF INTEGER SEQUENCES, cilt.21, sa.6, 2018 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 21 Sayı: 6
- Basım Tarihi: 2018
- Dergi Adı: JOURNAL OF INTEGER SEQUENCES
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
We give another proof of the Lucas-Lehmer test by using a singular cubic curve. We also illustrate a practical way to choose a starting term for the Lucas-Lehmer-Riesel test by trial and error. Moreover, we provide a nondeterministic test for determining the primality of integers of the form N = hp(n) - 1 for any odd prime p. We achieve these by using the group structure on a singular cubic curve induced from the group law of elliptic curves.