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Is it acceptable to write $x\in S\pmod m$ to denote "$x$ is congruent to a member of $S$ modulo $m$"? Are there any established alternatives to this notation?

An example of use: "When $m\ge 5$ is prime, solutions exist for all $p\notin \{0,\pm 1\} \pmod m$".

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The version below seems clear and standard:

When $m\ge 5$ is prime, solutions exist for all $p\not\equiv 0,\pm 1 \pmod m$

Also without negation:

When $m\ge 5$ is prime, solutions exist for all $p\equiv 0,\pm 1 \pmod m$

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