🧮 Algebra Problems

This section contains example problems and techniques for AMC 10 Algebra topics.

📚 All Problems

Number Theory & Divisibility

• Digit Sum Divisibility by 11 — Modular arithmetic and divisibility rules
• Find Least Positive Integer — Finding minimum values with constraints

Inequalities & Optimization

• Absolute Value Inequality — Case analysis and distance interpretation
• AM-GM Bounding Inequality — Arithmetic-geometric mean applications

Polynomials & Algebra

• Binomial Theorem Coefficient — Expanding and finding specific terms
• Perfect Square Discriminant — Quadratic discriminant analysis
• Remainder Theorem Synthetic — Polynomial division and remainders
• Symmetric Sum Identity Cubics — Vieta’s formulas and symmetric polynomials

Sequences & Series

• Linear Recursion Explicit — Finding closed forms for linear recurrences
• Newton Sum Symmetric — Power sums and Newton’s identities
• Telescoping Partial Fraction — Partial fraction decomposition

Functions & Equations

• Floor Function Bounding — Floor function properties and bounds
• Floor Sum Grouping — Summation with floor functions
• Functional Equation Plug X — Strategic substitution techniques
• Radical Exponent Manipulation — Working with radicals and exponents

🎯 Problem Types Overview

• Number Theory: Modular arithmetic, divisibility, least positive integers
• Inequalities: Absolute value, AM-GM, bounding techniques
• Polynomials: Remainder theorem, synthetic division, Vieta’s formulas
• Sequences: Arithmetic, geometric, telescoping series
• Functions: Floor functions, fractional parts, functional equations