[Math] the equal sign with 3 lines mean in Wilson’s theorem

notationself-learning

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.

Best Answer

$$(n-1)! \equiv -1\pmod n$$ 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".