i'm not sure if i understand this concept at all. for finding all the solutions (mod 45) of 4x=7 (mod 45), we know that solutions exist, b/c the gcd (4, 45)=1 which divides 7. then 4x= [52,97,112,157] (mod 45*4) 4x= 52 (mod 180) and 4x=112(mod 180). these reduce to x=13 (mod 45) and x=28 (mod 45) respectively. then x=13, 28 (mod 45)? i feel like i'm missing some important step or piece of the concept.