Modular Arithmetic
Introduction to Congruences
Congruences explore the number left over after division.
Requirements:
Divisibility
Difficulty:
2
Solving Linear Congruences
Solving for x in $ax ≡ b(mod n)$.
Requirements:
Bézout's Identity
Difficulty:
3
The Chinese Remainder Theorem
Solving systems of simultaneous congruences.
Requirements:
Linear Congruences
Difficulty:
3
Properties of Congruences
Defining Mathematical Operations mod m.
Requirements:
Linear Congruences
Difficulty:
3
Divisibility Tests
Finally, a proof for why divisibility rules work!
Requirements:
Congruences
Difficulty:
2
Euler's Totient Function
Counting numbers coprime to n.
Requirements:
Primes
Difficulty:
3
The Order of an Integer
How many times do you multiply before you get back to 1?
Requirements:
Euler's Totient Function
Difficulty:
3
Primitive Roots
Integers that can generate all others (mod p).
Requirements:
Euler's Theorem
Difficulty:
4
Quadratic Residues
Numbers that have square roots modulo n.
Requirements:
Modular Arithmetic
Difficulty:
4
⬅️ Back