I'm struggling with this one:
How many incongruent solutions are there to the congruence ?
I know I have to use Hensel's Lemma here. But the examples I've seen the mod is easily factored (e.g. , or ) so those examples aren't exactly the same as what is presented here I'm guessing since 144 is
Well if you count n distinct (that is, incongruent) solutions mod 2^4 and m distinct solutions mod 3^2, then the number of distinct solutions mod 144 is nm by CRT.
To be honest I've only worked a little bit with Hensel's lemma so if you have a hard time finding n and m I may not be of much help, in that case someone else will probably step in.