A Proof of the Lucas-Lehmer Test and its Variations by Using a Singular Cubic Curve

Date

2018-01-01

Author

Küçüksakallı, Ömer

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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.

Subject Keywords

Elliptic curve, Jacobi symbol, Dickson polynomial, Lucas sequence

URI

https://hdl.handle.net/11511/55366

Collections

Department of Mathematics, Article