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A natural number that cannot be formed by adding any two abundant numbers.

The number of integers coprime to a given positive integer less than the integer itself.

The largest positive integer that divides two or more integers without a remainder.

The numbers in a multiplication operation. For example, in 3 × 4 = 12, 3 and 4 are the _____, and 12 is the product.

A natural number that is strictly less than its sum of positive divisors, excluding itself.

A number whose prime factors are raised to powers different from those in another number.

A positive integer that is equal to or greater than the sum of its proper divisors except itself.

The integer $n$, in expressions like $a \equiv b \pmod{n}$, which defines the equivalence class of $a$ and $b$ in modular arithmetic.

The higher integer in a pair of consecutive primes that differ by six.

A set of integers in which every pair of integers has a greatest common divisor of 1.

A function of a positive integer $n$ that gives the sum of all positive integers less than $n$ that are coprime to $n$.

A positive integer that is equal to the sum of its proper divisors.

A natural number greater than 1 that is not a prime number nor a composite number, and only divisible by ±1 and itself.

Numbers that divide a given integer leaving no remainder.

A sequence of integers in which each number is the sum of the last two, starting from 0 and 1.

An integer $a$ is said to be this modulo $n$ if $a$ is non-negative and less than $n$.

Refers to an integer's ability to be represented as the sum of the cubes of its digits. 153 is such a number because $1^3 + 5^3 + 3^3 = 153$.

A natural number greater than 1 that is not prime, meaning it has more than two distinct positive divisors.

Prime numbers that differ by two.

An integer or polynomial that when raised to a specific power, yields the original number or polynomial under the operation of a specific modulus.

A theorem stating that the sum of the reciprocals of the prime numbers diverges.

An integer-valued polynomial expression of a number $n$ that is equal to the sum of the first $n$ positive integers.

A system of arithmetic for integers, where numbers wrap around upon reaching a certain value, called the modulus.

A relation between an integer $a$ and a positive integer $n$ such that $a$ and $n$ are divisible by the same prime numbers to the same powers.

A sequence of numbers where each number is the product of the previous number and any integer greater than one.

The ratio of two consecutive numbers in Fibonacci sequence tends to this value as they increase.

A positive integer composed of two or more prime numbers multiplied together.

A set of primes such that by appending another digit to the right, one obtains another prime.

An integer that is a divisor of the difference of two other integers.

A positive integer which is the sum of all positive divisors of another number, excluding the number itself.

The smallest positive integer that is divisible by each of two or more integers without a remainder.

A sequence of numbers, where each number is the sum of a specific set of previous numbers.

Two numbers for which their only common positive integer divisor is 1.

A sequence of numbers in which the difference between any two successive members of the sequence is a constant.

A number that can both be divided and divide another number exactly.

Positive integers greater than 1 that only have two distinct positive divisors: 1 and the number itself.

A prime number that remains prime when its digits are reversed.

Two numbers for which the sum of the proper divisors of one number is equal to the other number, and vice versa.

A natural number in the sequence $1, 1, 2, 3, 5, 8, 13, ...$, where each number after the first two is the sum of the two preceding ones.