FINAL EXAMINATION IN NUMBER THEORY

This means you add a and b, then find the remainder when divide by m.

• a + b mod m

• (a + b) mod m + b

• m Ξ a + b

• m mod a + b

Multiply a and b, and then find the remainder when divided by m.

• a x b mod m

• (a x b) mod m

• a x b mod m x b

• m Ξ a x b

Subtract b from a, and then add m if the result is negative. Then find the remainder when divided by m.

• a - b mod m

• b - a mod m - a

• a - b mod m - b

• m Ξ a - b

The following are the examples of Modular Arithmetic, except

• 9 mod 4 = 1

• 12 mod 3 = 2

• 7 mod 10 = 7

• -13 mod 4 = 3

Which is not a properties of Modular Arithmetic?

• Associative

• Commutative

• Distributive

• Comparative

(a+b)+c= a+(b+c) mod m

• Associative Property

• Commutative Property

• Cumulative Property

• Distributive Property

a+b= b+a mod m

• Associative Property

• Commutative Property

• Cumulative Property

• Distributive Property

a×(b+c)= (a×b)+(a×c) mod m

• Distributive Property

• Transitive Property

• Associative Property

• Commutative Property

Refers to the mathematical concept where two objects or shapes are the same in shape and size.

• Theory of Congruence

• Modulo

• Moduli

• Modulus

Refers to the relationship between two integers when their difference is divisible by a given integer.

• Congruences

• Modulus

• Transitive

• Associative