I am mostly a lazy person and so if I can reduce what I write, all the better. Obviously ultimately it is for the professor to decide whether something is or not an abuse in notation, but I want to know whether this is, at least, acceptable in the general case.
I have made the following statement:
Assume $n\equiv 2 \pmod5$:
Then $n^5\equiv2^5\pmod5 \implies n^5-n\equiv 2^5-2=30\equiv0 \pmod5 \implies n^5-n=5k$
for some $k\in\mathbb{N}$
The part I am unsure about is the equals sign followed by a congruency symbol. It seems to me readable enough, but I am very lax with notation.
Edit:
I know this is not the whole proof to my problem, there are 4 other cases to consider, but it's pretty much copy paste this assumption and change the numbers, it's explicetly the notation that I am conerned about.