Number Theory for Data Structures & Algorithms

Build the proof vocabulary behind reliable integer algorithms.

Turn Bézout identities into constructive algorithms.

Understand prime structure and enumerate multiplicative objects efficiently.

Precompute prime and factor information at scale.

Compute safely and efficiently in residue classes.

Solve one or many compatible modular constraints.

Test and factor large machine integers robustly.

Exploit multiplicativity and convolution to transform counting problems.

Evaluate combinatorial quantities under prime and composite moduli.

Use constructive integer methods for equations and best approximations.

Determine and construct modular roots.

Reason about modular operations through finite-group structure.

Accelerate recurrence evaluation with algebraic representations.

Turn polynomial operations into fast convolution primitives.

Compute in prime and extension fields using polynomial quotients.

Engineer arithmetic beyond native-word operations.

Connect finite-field groups to modern cryptographic primitives.

Combine arithmetic invariants with query and dynamic-programming structures.