Number Theory Quiz & Flashcards

11 is prime because it has no divisors other than 1 and itself, while the others can be divided by integers other than 1 and themselves.

The GCD of 8 and 12 is 4, as it is the largest number that divides both without a remainder.

9 is composite because it can be factored into 3 x 3, while the others are prime.

Coprime numbers have no common factors other than 1, which distinguishes them from other types.

The LCM of 4 and 5 is 20, the smallest number that both can divide evenly.

12 is abundant because the sum of its divisors (1, 2, 3, 4, 6) is greater than 12.

A perfect square is specifically defined as a number that can be expressed as the square of an integer.

Prime numbers cannot be expressed as a product of two primes; this is true for composite numbers.

The sum of the first 5 natural numbers (1 + 2 + 3 + 4 + 5) equals 15.

10 is a semiprime because it can be factored into two primes: 2 and 5.

Modular arithmetic is primarily used to calculate remainders when one number is divided by another.

All options are perfect cubes: 27 (3^3), 64 (4^3), and 125 (5^3).

Mersenne primes must be expressed as 2^p - 1, where p itself is also a prime number.

Parity specifically describes whether a number is even or odd.

The digital root is found by summing the digits (9 + 8 + 7 + 5 = 29, 2 + 9 = 11, 1 + 1 = 2) until one digit remains.

A quadratic residue modulo a prime is a number that can be expressed as the square of an integer within that modulus.

All integers can be expressed as fractions (e.g., n/1), but not all are even or prime.

Congruent numbers have the same remainder when divided by n, which defines their relationship.

√2 is irrational because it cannot be expressed as a fraction of two integers.

3^2 + 4^2 equals 9 + 16, which is 25.

A deficient number has a sum of its proper divisors that is less than the number itself.

The number 1 is known as the multiplicative identity because any number multiplied by 1 remains unchanged.

Not all prime numbers are odd; 2 is the only even prime number, countering the misconception.

6 is a perfect number because its proper divisors (1, 2, 3) sum to 6.

The next Fibonacci number after 13 is 21 (8 + 13).

Even numbers can be prime; for example, 2 is even and prime.

Numerical bases refer to the total number of unique digits used in a number system.

The digital root is 9, as it is obtained from the summation of the digits of 27 (2 + 7 = 9).

The prime factorization of 30 is 2 x 3 x 5.

A perfect square has an integer as its square root, by definition.

Odd numbers can be expressed in the form 2k + 1, where k is an integer.

1, 2, and 3 are all common factors of both 12 and 18.