Advanced (AIME)

Tackle olympiad-level ideas and harder AIME/USAMO crossover topics such as advanced number theory, geometry transformations, and deep algebraic methods.
Expect longer chains of reasoning and proof-oriented structure.

This section is currently under development. The content you see here is filler for now.

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Strong Number Theory

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Lifting the exponent, orders, and deeper divisibility arguments.

Strong Number Theory

Orders, lifting exponents, and tougher Diophantine equations for AIME.
Updated: 8 minutes ago

Advanced Counting

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Generating functions, bijections, and harder combinatorial arguments.

Advanced Counting

Bijections, recursion, and invariants for AIME-level counting.
Updated: 8 minutes ago

Polynomials & Roots

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Root bounding, irreducibility, and polynomial manipulation.

Polynomials and Root Techniques

Vieta's formulas, factor theorem, and root manipulation.
Updated: 8 minutes ago

Complex Numbers

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Advanced complex number techniques for AIME geometry and algebra.

Complex Numbers

Roots of unity, polar form, and geometric interpretations.
Updated: 8 minutes ago

Advanced Geometry

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Projective methods, inversions, homothety, and spiral similarity.

Advanced Geometry

Cevians, homothety, and power of a point for AIME.
Updated: 8 minutes ago

Sphere Geometry

Surface area, volume, and planar cross-sections.
Updated: 8 minutes ago

Angle Chasing Mastery

Systematic angle relationships in complex diagrams.
Updated: 8 minutes ago

Homothety and Spiral Similarity

Scaling and rotation transformations for advanced geometry.
Updated: 8 minutes ago

Trig in Contests

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Contest-specific trig tricks and identities.

Trigonometry in Contests

Identities, sine and cosine rules, and trig substitution.
Updated: 8 minutes ago

Inequalities (AIME)

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Schur, SOS, and multi-variable inequality techniques.

Inequalities (AIME Level)

Cauchy, Jensen (intro), and strategic substitutions.
Updated: 8 minutes ago

Generating Functions

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Using formal power series to solve counting problems.

Generating Functions (Intro)

Translate counting into algebra using power series.
Updated: 8 minutes ago

Functional Equations (AIME)

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Harder functional equations requiring injectivity and Cauchy-type analysis.

Functional Equations (AIME Level)

More sophisticated substitutions and invariants in FE problems.
Updated: 8 minutes ago