Answer all the questions below and press submit to see how many you got right.
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 $0\leq n<14$ satisfies $83\cdot 14+5\equiv n \mod{14}?$
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 2100?
What is the sum of the exponents in the prime factorization of 210?