Quote by trap101
Well that's great....Just so I'm on firm ground with the question:
1 + 1 + 1...........1 (is congruent to) ______ (mod p)
adding up all those one's will give me:
(p1) (congruent to) ______ (mod p)

Yes, the question is entirely clear. I'm frankly having a hard time believing that you are (presumably) at least a week or so into a universitylevel number theory course and you cannot show that (p  1) is congruent to 1 (mod p), unless you're just having silly moment. Think about the definitions of congruence you have posted (I personally think a = pk + b is easiest for this purpose, but of course they are all equivalent). Remember that k can be ANY integer.