What is a group in mathematics?
A Set of numbers
B Set with operations
C Set with one element
D Set with addition
Which of the following is true for a cyclic group?
A Every element can be written as a power of a single element
B Has no identity element
C Contains only one element
D Non commutative
What is the least common multiple (LCM) of 4 and 6?
A 36
B 6
C 24
D 12
What does the mod operation in modular arithmetic return?
A A product of numbers
B A number’s square
C A remainder after division
D A sum of values
Which of the following is the identity element for multiplication in number theory?
A 2
B 1
C 0
D -1
What is the inverse of 2 modulo 7?
A 4
B 3
C 1
D 2
Which of the following is a property of a group under addition?
A Contains no inverse
B Non commutative
C Contains no identity
D Commutative
Which of the following is true about prime numbers?
A They are divisible by 2
B They have exactly three divisors
C They are divisible by only 1 and themselves
D They can be negative
What is the greatest common divisor (GCD) of 24 and 36?
A 24
B 12
C 6
D 36
What does the Chinese Remainder Theorem help solve?
A Modular arithmetic problems
B Matrix equations
C Linear equations
D Complex number problems
What is the order of an element in a group?
A The largest divisor of the group
B The highest power of the element
C The smallest number of operations to return to identity
D Number of elements in the group
What is a perfect number?
A A number whose digits add up to 10
B A number divisible by itself
C A number with no divisors
D A number equal to the sum of its divisors excluding itself
In group theory, what does a cyclic group have?
A Elements formed by a single generator
B Infinite elements
C Non associative operation
D A finite number of generators
Which of the following is true for modular arithmetic?
A It involves the addition of matrices
B It works with negative remainders
C It always results in a positive result
D It deals only with fractions
What is the result of 5^3 mod 7?
A 4
B 5
C 2
D 6