All Prime Numbers Have Primitive Roots

Ruben Gamboa
(University of Wyoming)
Woodrow Gamboa
(Stanford University)

If p is a prime, then the numbers 1, 2, ..., p-1 form a group under multiplication modulo p. A number g that generates this group is called a primitive root of p; i.e., g is such that every number between 1 and p-1 can be written as a power of g modulo p. Building on prior work in the ACL2 community, this paper describes a constructive proof that every prime number has a primitive root.

In Rob Sumners and Cuong Chau: Proceedings Seventeenth International Workshop on the ACL2 Theorem Prover and its Applications (ACL2 2022), Austin, Texas, USA, 26th-27th May 2022, Electronic Proceedings in Theoretical Computer Science 359, pp. 9–18.
Published: 24th May 2022.

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