Commands mod, bmod, pmod, pod are provided by the amsopn package to deal with the special spacing conventions of ``mod'' notation. bmod and pmod are available in /, but with the amsopn package the spacing of pmod will adjust to a smaller value if it's used in a non-display-mode formula. mod and pod are variants of pmod preferred by some authors; mod omits the parentheses, whereas pod omits the ``mod'' and retains the parentheses.
\gcd(n,m\bmod n);\quad x\equiv y\pmod b ;\quad x\equiv y\mod c;\quad x\equiv y\pod d