Concepts
What visual is typically used to represent modulo?
A clock
1
What CAN'T you when solving linear congruencies?
Divide numbers on each side
What does Congruency mean in modulo?
2 values have the same remainder
Solve -16(mod 6)
2
ax ≡ b (mod m)
If GCD (a,m) > 1, what are the 2 options in terms of solutions?
Mutliple solutions or none!
Generally, how do you find the inverse?
Guess and check
Solve (12+27)mod 4
3
How many distinct solutions does 15x ≡ 25 (mod 80) have?
5
What are the 4 operations you can do with Modulo?
(Bonus there's 1 more!)
Addition, Subtraction, Multiplication, Exponentiation
Bonus: Adding multiples
Solve (33*275)mod 8
3
1. Solve 3x = 7 (mod 4)
2. What is the longest river on Earth?
1. x= 1(mod 4)
2. The Nile
What is the residue often referred to as? (Be specific!)
The smallest non-negative residue/remainder
Solve 35^5(mod 6)
5
1. How many distinct solutions does 25x ≡ 2 (mod 15) have?
2. Which blood type is the universal donor?
1. None.
2. O-type blood.