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Congruence : Two shapes are called congruent if they have the same shape and size. Two integers are called congruent modulo $x$ if they have the same remainder in a division by $x.$
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.
Which integer $n$ with $0\leq n<4$ satisfies $24\equiv n \mod{4}?$
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.
What is the sum of the exponents in the prime factorization of 44100?
What is the prime factorization of 2160?