Seeking after notation for two objects equal up to a constant Sometimes we want to express that two objects are equal up to a constant but there is no need to keep writing out the constant or constants. For example, often times the constant or constants involved in the derivation of a primitive of a function plays or play a role unimportant. 
I wonder if there is a convenient, established notation for such a matter. I thought of using modular notation. But using that does not simplify because I still have to mention "modulo-what". 
If possible, some variants of the equality sign are preferable. For instance, if the constant of proportionality is unimportant then it may be suppressed by using $\propto.$ In this sense I mean by saying that some variants of the equality sign are preferable. 


two objects are equal up to a constant

The answer might depend on what the objects are, and what operation is applied to the object and the constant.
But congruence could be a good fit.  To quote wikipedia:

$37$ and $57$ are congruent modulo $10$,
$ 37 \equiv 57 \pmod {10} $
since $37 − 57 = − 20$ is a multiple of $10$

If you explicitly define your notation and stay consistent, then it is fine to just use the $\equiv$ symbol without the$\pmod n$.
There are other kinds of congruence with different notation.  But, as above, congruence in abstract algebra is usually denoted as a triple-struck equals sign $\equiv$.
