Tuesday
July 28, 2015

Homework Help: ***Discrete Math ***

Posted by Jane on Friday, November 23, 2007 at 5:26pm.

I'm not sure how to start part(a). I believe part (b) is correct, but just in case I would like to make sure it's correct.

(a) Explain p^(q-1) = 1 modq , If p and
q are distinct primes.
Ans: I was thinking of doing
something like part (b) but I
felt it was somehow wrong
because I wouldn't know how to
go from there.

(b) Determine 17^(98) mod 7 (give
answer in mod 7)

Ans: a=17, p=7 a^(p-1)=1 mod p
==> 17^6 = 1 mod 7
[17]^6 = [1]

[17]^98= [(17)^6]^(16) * (17)^2
\__________/
|
[1]^16 * [17]^2 = 289
Therefore, 17^98 = 289 mod7

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