Constellation

Core arithmetic identities — the building blocks of number theory that underpin every Erdos problem.

Inequalities and ordering on naturals — essential for bounding arguments in Erdos distance problems.

Divisibility relations — core to Erdos-Straus conjecture and arithmetic progression problems.

Logical foundations — the proof strategies needed for contradiction and case-analysis arguments.

Existence proofs and witnesses — the pigeonhole-style arguments behind cap set and Ramsey results.

Exponentiation properties — additive basis problems and power-sum conjectures.

Operations on finite structures — sum-free sets and subset counting arguments.

Decidable propositions — the computational side of graph coloring and Ramsey theory.

Function properties — iterated function arguments used in Ramsey number bounds.

Inductive structure of naturals — the backbone of every Erdos number theory proof.