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In this document: http://cims.nyu.edu/~kiryl/teaching/aa/les092603.pdf

The ordered pair notation is used but it is never explained what it means.

ex:

Corollary: Let p be a prime. Then
n^(p−1) ≡ 1 mod p
for any integer n ≥ 1 with (n, p) = 1.

Does anyone know what (a,b) signifies in this context?

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$(a,b)$ denotes the $\gcd(a,b)$. In this context, $(n,p) = 1 \implies$ $p$ and $n$ are relatively prime and since $p$ is a prime, this means $p$ does not divide $n$.

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This means, in my experience, that $n$ and $p$ are relatively prime- i.e., $(n,p)=gcd(n,p) $.

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