Modular Arithmetic

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Modular Arithmetic

Part 1

• What is a Modulus?
• Modular Arithmetic
• The Pigeonhole Principle
• Problem Solving with Modular Arithmetic
• Fermat's Little Theorem
• Euler's Theorem
• Lagrange's Theorem
• Wilson's Theorem
• Chinese Remainder Theorem
• Wolstenholme's Theorem
• Problem Solving 1

Part 2

• Sophie Germain's Theorem
• Quadratic Residues
• Primitive Roots Modulo p
• Legendre's Symbol
• Quadratic Reciprocity
• Problem Solving 2

For Enthusiasts

• Fast Matrix Multiply
• Minkowski's Convex Body Theorem

Teacher's Notes

• About this Book
• Common Student Errors

Credits

• Thanks to High School Mathematics Extensions/Further Modular Arithmetic from which much of this material was adapted.
• Thanks to Wikipedia for original version of content on Quadratic reciprocity.