Quiz 1-3_Abstract

In modular arithmetic, is it always true that (a + b) mod m = (a mod m) + (b mod m)?

• No, it depends on the values of a, b, and m

• Yes, this is always true

• Only if a and b are relatively prime to m

• Only if m is a prime number

Find (8 * 3) mod 7.

• 1

• 3

• 24

• 56

If 2x ≡ 8 (mod 6), what is the solution for x?

• 2

• 3

• 4

• 5

Find the modular multiplicative inverse of 2 modulo 11.

• There is no inverse

• 1

• 2

• 6

What is the remainder when 17 is divided by 4?

• 1

• 2

• 3

• 4

Solve the congruence: x ≡ 17 (mod 12).

• 5

• 17

• 29

• There is no solution

If a ≡ b (mod m) and c ≡ d (mod m), is it always true that (a + c) ≡ (b + d) (mod m)?

• No, it depends on the values of a, b, c, d, and m

• Yes, this is always true.

• Only if a and c are relatively prime to m

• Only if b and d are relatively prime to m

For a given set of triangles, the relation of 'is similar to ()' and 'is congruent to ()' not shows equivalence.

• True

• False

Modular arithmetic is useful in various applications. Which of the following is NOT a common use case?

• Error detection in data transmission

• Public-key cryptography

• Clock arithmetic (e.g., 12-hour clock)

• Direct calculation of square roots

He is a German Mathematician who gave the modern definition of function in 1837.

• Peter Derichlet

• Peter Direchlet

• Peter Dirichlet

• Peter Derechlet