What is the equal sign with 3 lines mean in Wilson's theorem?
I'm reading up on Wilson's Theorem, and see a symbol I don't know... what does an equal sign with three lines mean?
I'm looking at the example table and I still can't infer what they are trying to say about that relationship between equations.
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$\begingroup$$$(n-1)! \equiv -1\pmod n$$ means that $(n-1)!$ and $-1$ differ by a multiple of $n$. Or, if you prefer, that $(n-1)!+1$ is a multiple of $n$.
In general, $$a\equiv b\pmod n$$ means that $a$ and $b$ differ by a multiple of $n$, or that $a-b$ is a multiple of $n$.
It's explained in detail in the Wikipedia article on "modular equivalence". The $\equiv$ symbol itself is pronounced "is equivalent to".
$\endgroup$ 2 $\begingroup$Wilson's Theorem:
$$(n-1)!\ \equiv\ -1 \pmod n.$$
It means "is congruent to" (modulo n): that is, $$(n - 1)! -(-1) = (n - 1)! + 1 \equiv 0 \pmod n$$ And that simply means that $n$ divides $(n - 1)! + 1$.
$\endgroup$ 2 $\begingroup$a ≡ b (mod n)
is equivalent to
a mod n = b :(if b less than n)
a mod n = b mod n :(else)
(I am not sure, if also b>0).
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