Fermat's little theorem : Fermat's little theorem says that for a prime number $p$ and a natural number $x$ with $0\lt x\lt p$ we have $x^{p-1} \equiv 1 \mod{p}.$ For example if $p=5$ and $x=2$ we have $2^{5-1}=16 \equiv 1 \mod{5}.$

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 $m.$

One seventh : One seventh is the number $\frac{1}{7}=0.\overline{142857}.$

Derivative : A derivative of $f$ also written as $f^{\prime}$ or $\frac{d}{dx}f$ or $\frac{df}{dx}$ is defined by $f^{\prime}(x)=\lim \limits_{h\to 0}\frac{f(x+h)-f(x)}{h}.$ The derivative $f^{\prime}(x)$ can be interpreted as the speed at which the function value is changing or as the slope of the tangent in the graph of $f$ at $x$. For example the derivative of a constant function is 0, the derivative of $f(x)=x$ is 1 and the derivative of $x^2$ is $2x.$ All local extrema of differentiable functions $f$ are roots of the derivative of $f.$

Linear Taylor approximation : The linear Taylor approximation at $x_0$ of a differentiable function $f$ is given by: $f(x_0)+f^{\prime}(x_0)(x-x_0).$

Bound : A bound refers to a level that is not exceeded by a function or sequence (upper bound) or a level that a function or sequence does not go below (lower bound). For example the function $f(x)=x^2$ has a lower bound of 0 but no upper bound. The function $f(x)=\sin x$ has an upper bound of 1 and a lower bound of -1.

Even : Even can refer either to an even function or an even number.

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Odd : In mathematics odd can refer either to an odd function or an odd number.

Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$

Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.