I recommend the notation $$ a \equiv_n b $$ in place of $a \equiv b \pmod{n}$. It's much less verbose. The meaning is clear. And the $n$ is where it really belongs, next to the $\equiv$ it is describing.

We're stuck with $a \equiv b \pmod{n}$ as the standard notation (for now!), because that's what Gauss came up with. I've got nothing against Gauss for not using a subscript $\equiv_n$. It seems to me that Disquisitiones Arithmeticae doesn't have subscripts anywhere. Subscripts must have been outside the graphic design space or something. So I don't blame him for resorting to $a \equiv b \pmod{n}$. Gauss did a great thing by popularizing $n \mid a-b$ as an equivalence relation of $a$ and $b$. But if we were to invent the notation today, I dare say $a \equiv_n b$ would be the modern choice. (See this post on Math.SE, where Alexander Gruber suggests the same thing in a comment.)

Of course, if there's no ambiguity, you can still just write plain $a \equiv b$. I'm talking about the cases where you need to or want to indicate the modulus $n$. It may not seem like much, but "(mod n)" is surprisingly verbose to physically write. If you're hand-writing pages or blackboards full of congruences, chances are you've already succumbed to abbreviating "(mod n)" somehow. I've seen lots of different shorthand, based on dropping the parenthesis, or some or all of the text "mod" (which is itself an abbreviation of "modulo", or if you really go by Gauss's Latin, "secundum modulum" - be thankful you're not writing that): \begin{align} a &\equiv b \quad \mathrm{mod}\ n \\ a &\equiv b \quad (\mathrm{m}\ n) \\ a &\equiv b \quad (n) \\ \end{align}

I've seen all of these used before, as well as $a \equiv_n b$. Certainly $a \equiv_n b$ is the cleanest notation.

As a free bonus, you get a cool-looking Fermat's theorem: $$ a^p\!\equiv_p\!a. $$

I recommend the notation $$ a \equiv_n b $$ in place of $a \equiv b \pmod{n}$. It's much less verbose. The meaning is clear. And the $n$ is where it really belongs, next to the $\equiv$ it is describing.

We're stuck with $a \equiv b \pmod{n}$ as the standard notation (for now!), because that's what Gauss came up with. I've got nothing against Gauss for not using a subscript $\equiv_n$. It seems to me that Disquisitiones Arithmeticae doesn't have subscripts anywhere. Subscripts must have been outside the graphic design space or something. So I don't blame him for resorting to $a \equiv b \pmod{n}$. Gauss did a great thing by popularizing $n \mid a-b$ as an equivalence relation of $a$ and $b$. But if we were to invent the notation today, I dare say $a \equiv_n b$ would be the modern choice. (See this post on Math.SE, where Alexander Gruber suggests the same thing in a comment.)

Of course, if there's no ambiguity, you can still just write plain $a \equiv b$. I'm talking about the cases where you need to or want to indicate the modulus $n$. It may not seem like much, but "(mod n)" is surprisingly verbose to physically write. If you're hand-writing pages or blackboards full of congruences, chances are you've already succumbed to abbreviating "(mod n)" somehow. I've seen lots of different shorthand, based on dropping the parenthesis, or some or all of the text "mod" (which is itself an abbreviation of "modulo", or if you really go by Gauss's Latin, "secundum modulum" - be thankful you're not writing that): \begin{align} a &\equiv b \quad \mathrm{mod}\ n \\ a &\equiv b \quad (\mathrm{m}\ n) \\ a &\equiv b \quad (n) \\ \end{align}

I've seen all of these used before, as well as $a \equiv_n b$. Certainly $a \equiv_n b$ is the cleanest notation.

As a free bonus, you get a cool-looking Fermat's theorem: $$ a^p\!\equiv_p\!a. $$