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Ansatz7
#15
Feb27-12, 09:49 PM
P: 29
Quote Quote by trap101 View Post
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:

(p-1) (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 university-level 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.