Advanced Geometric Inequalities
Ptolemy's theorem, advanced locus
Complex Diophantine Equations
Non-linear integer solutions
Expected Value & Recursive Probability
Markov chains, expected states
Functional Equations
Solving f(x) relationships
Advanced Modular Arithmetic
Fermat's Little Theorem, congruences
Combinatorics (Stars & Bars)
Inclusion-exclusion, advanced distributions
Vieta's Formulas & Polynomials
Relationships between roots and coefficients
Advanced Counting & Probability
Permutations, combinations
Creative Geometry
Unconventional area problems
Number Theory Basics
Divisibility rules, prime factorization