APMO · 3. Functional equations
Find and write complete proofs for functional equations: substitutions and squeezing, integer-valued functions, iteration and amplification, additivity and injectivity.
Choose substitutions that produce useful equalities and squeeze two-sided conditions.
Solve functional equations on positive integers with divisibility and induction.
Use equal arguments, iteration and amplification to prove an expected answer is the only one.
Derive additivity and injectivity and use side conditions correctly.
Write both halves of every 'find all functions' proof.