Math -> Lucas Theorem And Large Binomial Mod Prime

Prime-mod binomial coefficients beyond one factorial table, using base-p digit decomposition and Lucas theorem when n crosses p.

• Topic slug: math/lucas-theorem
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 1
• Repo companion pages: 3
• Curated external problems: 2

Microtopics

• lucas-theorem
• base-p-digits
• large-binomial
• prime-mod-binomial
• digit-product
• factorial-table-boundary

Learning Sources

Source	Type
cp-algorithms binomial coefficients	Reference
AtCoder ABC251 editorial	Reference
Competitive Programmer's Handbook	Reference

Practice Sources

Source	Type
Library Checker Binomial Coefficient (Prime Mod)	Practice
Kattis Odd Binomial Coefficients	Practice

Repo Companion Material

Material	Type
Lucas Theorem hot sheet	quick reference
Binomial Coefficient (Prime Mod)	flagship note
Template Library exact starter route	starter route

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Binomial Coefficient (Prime Mod)	Library Checker	Medium	Binomial Coefficients	Math; Implementation	Modular Arithmetic; Factorial Binomial; Base Conversion	Binomial Coefficient; Prime Modulus	A clean benchmark for the route split between one ordinary factorial table and Lucas digit decomposition under one prime modulus.

Stretch

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Odd Binomial Coefficients	Kattis	Hard	Binomial Coefficients, Pascal Structure	Math; Observation	Lucas Theorem; Bitwise Reasoning	Parity; Bitwise Pattern	A strong compare point where Lucas with p = 2 exposes a structural parity pattern instead of only answering one binomial query.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
BINOMIALCOEFFICIENTPRIMEMOD	Binomial Coefficient (Prime Mod)	primary	medium	-	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py