Number Theory and Algebra
Description: This quiz covers various concepts related to Number Theory and Algebra, including properties of integers, modular arithmetic, polynomials, and group theory. | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: number theory algebra modular arithmetic polynomials group theory |
Which of the following is a prime number?
Find the greatest common divisor (GCD) of 24 and 36 using the Euclidean algorithm.
Solve the modular equation 3x ≡ 5 (mod 7).
Factorize the polynomial x^3 - 2x^2 - 5x + 6.
Find the order of the element 3 in the group (Z_7, +).
Which of the following is a field?
Find the number of solutions to the equation x^2 + 2x + 1 = 0 in the field of complex numbers.
Which of the following is a cyclic group?
Find the multiplicative inverse of 7 in the field of integers modulo 11.
Which of the following is a prime ideal in the ring of integers?
Find the number of elements in the group U(10).
Which of the following is a subgroup of the group (Z_12, +)?
Find the characteristic of the field GF(2^8).
Which of the following is a normal subgroup of the group (S_3, *)?
Find the number of generators of the cyclic group of order 15.