Exploring Modular Arithmetic

What is the result of 15 mod 4?

• 4

• 3

• 2

• 1

Solve the congruence 3x ≡ 12 (mod 9).

• x ≡ 1 (mod 3)

• x ≡ 5 (mod 3)

• x ≡ 2 (mod 3)

• x ≡ 4 (mod 3)

Find the modular inverse of 7 modulo 26.

• 14

• 21

• 15

• 9

Prove that if a ≡ b (mod m), then a^2 ≡ b^2 (mod m).

• a^2 ≡ b (mod m)

• a^2 + b^2 ≡ 0 (mod m)

• a^2 - b^2 ≡ 1 (mod m)

• a^2 ≡ b^2 (mod m)

What is the smallest positive integer x such that 5x ≡ 1 (mod 12)?

• 5

• 9

• 7

• 3

If 8x ≡ 4 (mod 10), what is the value of x?

• 1

• 5

• 3

• 7

Show that 14 is congruent to 2 modulo 12.

• 14 is not congruent to 2 modulo 12.

• 14 is congruent to 0 modulo 12.

• 14 is congruent to 10 modulo 12.

• 14 is congruent to 2 modulo 12.

Find the modular inverse of 11 modulo 26 using the Extended Euclidean Algorithm.

• 7

• 19

• 14

• 23

If a ≡ b (mod m) and c ≡ d (mod m), what can be said about a + c and b + d?

• c + d ≡ b + d (mod m)

• a + c ≡ d (mod m)

• a + c ≡ b + d (mod m)

• a + c ≡ b (mod m)

Solve for x in the equation 4x ≡ 1 (mod 11).

• 7

• 5

• 2

• 3