Elliptic-curve Frobenius traces as primitive roots
Elliptic-curve Frobenius traces as primitive roots. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
Editorial MSC2020 mapping of Elliptic-curve Frobenius traces as primitive roots. https://ems.press/content/serial-article-files/52435#page=58 Not an author-supplied code.
Problem statement
For an elliptic curve , set at primes of good reduction. Are there infinitely many such primes for which is a primitive root modulo ?
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Background
Editorial question summary. Consult the linked source for the complete model, assumptions and discussion.
Progress & source assessment
Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.
- [1]Problem-session contributors; compiled by Thomas F. Bloom. Oberwolfach 2025 — Analytic Number Theory Problem Session (2025).; Elliptic-curve Frobenius traces as primitive roots linkCC BY-SA 4.0; source contributors, compiled by Thomas F. Bloom. These attributed adaptations are available under the same license.
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Discussion
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