Math -> Primitive Root

Find one generator of the nonzero residues modulo prime p by factoring p - 1 and rejecting candidates whose reduced-order powers collapse to 1.

• Topic slug: math/primitive-root
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 1
• Repo companion pages: 4
• Curated external problems: 2

Microtopics

• primitive-root
• generator
• cyclic-group-mod-prime
• factor-p-minus-one
• order-test
• discrete-root-boundary

Learning Sources

Source	Type
cp-algorithms primitive root	Reference
OI Wiki Primitive Root	Reference

Practice Sources

Source	Type
Library Checker Primitive Root	Practice
Library Checker K-th Root Mod	Practice

Repo Companion Material

Material	Type
Primitive Root hot sheet	quick reference
Primitive Root	flagship note
Template Library exact starter route	starter route
BSGS / Discrete Log	compare point

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Primitive Root	Library Checker	Hard	-	Math; Implementation	Modular Arithmetic; Fast Power; Prime Factorization	Generator; Prime Modulus; Factorization	The cleanest verifier for the repo's exact route: factor p - 1, then reject candidate generators whose reduced-order powers collapse to 1.

Stretch

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
K-th Root Mod	Library Checker	Hard	Discrete Root	Math; Implementation	Primitive Root; Discrete Log; Modular Arithmetic	Discrete Log; Linear Congruence In Exponents	The natural follow-up once generator finding is trusted and the learner is ready to reduce x^k ≡ a (mod p) to exponent arithmetic.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
PRIMITIVEROOT	Primitive Root	primary	hard	-	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py