Pick at least 4 operations that you can do in bashisms-free shell scripts:
$((n+1)) $((n>8)) $((n^4)) $((--n)) $((n*=5)) $((n++)) $((n==1?2:3))
The POSIX:2001 standard defines the arithmetic expansion requirements, which leads us to selecting all of the above operations except two:
"--" and "++" are not required to be implemented, and in some cases they may lead to unexpected results, such as the following:
$ bash -c 'n=1; echo $((++n))'
$ dash -c 'n=1; echo $((++n))'
Remember, if you rely on any non-standard behaviour or feature make sure you document it and, if feasible, check for it at run-time.