Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Integer : An integer is any ot the numbers $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots.$

Modulo : In number theory a whole number $x$ is congruent to a whole number $y$ modulo a natural number $m$, also written as $x \equiv y \mod{m}$ if $x$ and $y$ have the same remainder in the division by $m$ or equivalently if $(x-y)$ is divisible by $m.$

Remainder : In the division of a whole number $x$ by a natural number $y$ the remainder is the unique whole number $r$ with $0\leq r\lt y$ with $x=m\cdot y+r$ for some whole number $m.$ The remainder is the number of leftover wholes in the division. For example the remainder of the division of 14 by 3 is 2 as $14=4\cdot 3+2.$ Remainders are fundamental for the concept of congruence modulo $y$ in number theory.

Prime factorization : A prime factorization of a natural number writes the natural number as a product of prime factors. A prime factorization is usually stated in the form $n=\prod p_i^{n_i}.$ For example the prime factorization of 12 is $12=2^2\cdot 3.$ The fundamental theorem of arithmetic says that every number has a unique prime factorization (disregarding the order of the factors).

Exponent : In a power $a^x$ the number $x$ is called the exponent of the power.

Number : A number $x$ is a mathematical symbol representing a quantity.

Prime factor : A prime factor is a factor that is a prime number.

Prime factorization : A prime factorization of a natural number writes the natural number as a product of prime factors. A prime factorization is usually stated in the form $n=\prod p_i^{n_i}.$ For example the prime factorization of 12 is $12=2^2\cdot 3.$ The fundamental theorem of arithmetic says that every number has a unique prime factorization (disregarding the order of the factors).

Sum : A sum is the result of an addition.