A Nice Algebra problem from Russia | Inequality Proofs | Geendle

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This comprehensive list covers a wide range of topics that can be addressed in math-related content.
Algebra:
Equations
Inequalities
Polynomials
Functions
Systems of Equations
Exponential and Logarithmic Functions
Geometry:
Euclidean Geometry
Coordinate Geometry
Trigonometry
Geometric Transformations
Solid Geometry
Geometric Proofs
Calculus:
Limits
Derivatives
Integrals
Differential Equations
Multivariable Calculus
Sequences and Series
Statistics and Probability:
Descriptive Statistics
Inferential Statistics
Probability Theory
Random Variables
Probability Distributions
Hypothesis Testing
Linear Algebra:
Vectors
Matrices
Determinants
Eigenvalues and Eigenvectors
Vector Spaces
Linear Transformations
Number Theory:
Divisibility
Prime Numbers
Modular Arithmetic
Diophantine Equations
Cryptography
Fermat’s and Euler’s Theorems
Discrete Mathematics:
Combinatorics
Graph Theory
Logic
Set Theory
Algorithms
Boolean Algebra
Topology:
Topological Spaces
Continuity
Compactness
Homotopy
Fundamental Group
Manifolds
Functional Analysis:
Banach Spaces
Hilbert Spaces
Linear Operators
Normed Spaces
Spectral Theory
Fourier Analysis
Mathematical Logic:
Propositional Logic
Predicate Logic
Model Theory
Proof Theory
Set Theory
Computability Theory
Abstract Algebra:
Groups
Rings
Fields
Modules
Galois Theory
Homomorphisms
Applied Mathematics:
Numerical Analysis
Optimization
Differential Equations
Mathematical Modeling
Control Theory
Game Theory
Recreational Mathematics:
Puzzles
Magic Squares
Mathematical Games
Mathematical Paradoxes
Mathematical Art
Fractals
History of Mathematics:
Ancient Mathematics
Medieval Mathematics
Renaissance Mathematics
Modern Mathematics
Biographies of Mathematicians
Development of Mathematical Theories
Mathematics in Computing:
Algorithms
Data Structures
Computational Complexity
Cryptography
Information Theory
Machine Learning
Mathematics in Natural Sciences:
Mathematical Physics
Mathematical Biology
Mathematical Chemistry
Environmental Mathematics
Financial Mathematics
Actuarial Science
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