Math -> Modular Arithmetic

Safe modular computation: powers, inverses, congruences, and the algebra needed to avoid overflow and mistakes.

• Topic slug: math/modular-arithmetic
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 4
• Repo companion pages: 2
• Curated external problems: 8

Microtopics

• modpow
• modinv
• Fermat
• Euler-theorem
• congruences
• mod-division

Learning Sources

Source	Type
MIT 6.857 modular arithmetic review	Course
USACO Guide modular arithmetic	Reference
cp-algorithms modular inverse	Reference

Practice Sources

Source	Type
CSES Exponentiation	Practice
CSES Exponentiation II	Practice
Kattis Modular Arithmetic	Practice

Repo Companion Material

Material	Type
Number theory cheatsheet	quick reference
Templates overview	template guide

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Exponentiation	CSES	Easy	Fast-Exponentiation, Mod Arithmetic	Implementation; Math	Modular Arithmetic; Binary Exponentiation	Binary Exponentiation; Pow	Canonical modular fast-power warmup.
Distributing Apples	CSES	Easy-Medium	Stars And Bars, Mod Arithmetic	-	-	Combinations; Distributions	Simple counting with modular binomial coefficients.
Binomial Coefficients	CSES	Medium	Combinatorics/Counting-Basics, Mod Inverses, Combinatorics	Math; Precomputation	Factorials; Modular Inverse; Combinations	Ncr; Factorials; Modular Inverse; Inverse Factorials	Standard modular combinations with precomputation.
Creating Strings II	CSES	Medium	Factorials, Mod Inverses	-	-	Multiset Permutations; Combinatorics; Mod Arithmetic	Distinct-string counting via modular combinatorics.
Exponentiation II	CSES	Medium	Fast-Exponentiation, Mod-Inverse, Totient Tricks	Implementation; Number Theory	Binary Exponentiation; Modular Arithmetic; Fermat's Little Theorem	Tower Exponentiation; Fermats-Little-Theorem; Mod Arithmetic; Phi	Adds exponent towers and modulus reduction logic.

Stretch

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Counting Grids	CSES	Hard	Combinatorics/Bracelet-Counting	Combinatorics; Algebra	Modular Arithmetic; Symmetry Counting	Burnside; Pólya Counting; Mod Arithmetic	A stronger symmetry-counting problem that rewards comfortable modular evaluation.
Counting Necklaces	CSES	Hard	Combinatorics/Burnside	Combinatorics; Number Theory	Modular Arithmetic; Group Actions; GCD/LCM Basics	Burnside; Group Actions; Mod Arithmetic	A canonical advanced counting problem where modular arithmetic sits inside Burnside's lemma.
Graph Paths I	CSES	Hard	Matrix-Exponentiation	Graphs; Math	Modular Arithmetic; Matrix Multiplication; DP On Walks	Graph Walks; Mod Arithmetic	A classic matrix-exponentiation application where the answer is required modulo a prime.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
COUNTINGNECKLACES	Counting Necklaces	secondary	hard	burnside lemma; rotation symmetry; orbit counting	Note	Code
DISTRIBUTINGAPPLES	Distributing Apples	secondary	medium	stars and bars; single binomial query; factorial precompute	Note	Code
EXPONENTIATION	Exponentiation	primary	easy	binary exponentiation; repeated squaring; modular fast power	Note	Code
EXPONENTIATION2	Exponentiation II	primary	medium	binary exponentiation; fermat exponent reduction; zero exponent edge case	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py