Which Statements of congruence are true and which are false and why?

Question

177 _= 17 (mod 8)
871 _= 713 (mod 29)
1322 _= 5294 (mod 12)
5141 _= 8353 (mod 11)
13944 _= 8919 (mod 13)
67 x 73 _= 1 x 3 (mod 5)
17 x 18 x 19 x 20 _= 4! (mod 8)
83 (144 power) _= 15 (144 power) (mod 17)
Their not equals signs...they are three lines on top of one another.

Answer 1

177-17 = 160 = 20*8 true
871-713 = 158 false
1322-5294 = -3972 = -331*12 true
and so on
17*18*19*20/4! = 17*3*19*5 false
83 = 15 (mod 17), so true