Hem a+b+c=d+e+f olsun, hem de a²+b²+c²=d²+e² f²

Mind map summary: Equations & Numbers

Pythagorean Triples
- Basic Concept
  - Integer Sides
  - Examples
- Extensions
  - a²+b²=c²+d²
  - All Different
Factorization Method
- Difference of Squares
  - a²-c²=d²-b²
- Finding Examples
  - 24 Case
  - 27 Case
Cyclic Quadrilaterals
- Right Angles
  - Opposite Angles
- Ptolemy's Theorem
  - Diagonal Formula
- Geometric Properties
  - Inscribed Circle
Equal Perimeters
- Impossibility Proof
  - Constraint Analysis
  - ab=cd Requirement
- Real vs Integer
  - Degree Elevation
Three-Variable Case
- a+b+c=d+e+f
  - Sum Equality
- a²+b²+c²=d²+e²+f²
  - Grouping Strategy
  - ab=cd Solution
- Complete Solution
  - Example 1,6,5
  - Verification
Higher Powers
- Cubes Challenge
  - Open Problem
- Eight Variables
  - Multi-Power Equality
  - Infinite Solutions

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