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Defines a CSS class in the preamble which styles the \"Lemma\" environment, used in the statement.
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\nLet $p$ be a prime number, and assume $p$ divides the product of two integers $a$ and $b$.
Then $p|a$ or $p|b$ (or both).
Let $D = \\{z : |z| \\lt 1\\}$ be the open unit disk in the complex plane $\\mathbb{C}$ centered at the origin and let $f : D \\to D$ be a holomorphic map such that $f(0) = 0$.
\nThen, $|f(z)| \\leq |z|$ for all $z$ in $D$ and $|f'(0)| \\leq 1$.
\nMoreover, if $|f(z)| = |z|$ for some non-zero $z$ or $|f'(0)| = 1$, then $f(z) = az$ for some $a$ in $\\mathbb{C}$ with $|a| = 1$.
\nThis part demonstrates a binding between the properties of an element in the graph and values entered in the answer boxes.
\nPlace the dot at $(\\var{a},\\var{b})$. You can either drag the dot or enter coordinates in the box.
\n\n$X$: [[0]], $Y$: [[1]]
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\n\nIs this function odd or even, or neither? You can drag the point labelled $f(x)$ and compare it with the point labelled $f(-x)$.
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\nDefine a function $f(t)$ on $[0,2\\pi)$ which plots in polar coordinates a Lemniscate of Bernoulli touching the points $(-5,0)$, $(0,0)$ and $(5,0)$.
\n$f(t) = $ [[0]]
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