Hint for Number Theory homework
1) find the pattern of the following:
a) (3^10) modulo 11
b) (2^12) modulo 13
c) (5^16) modulo 17
d) (3^22) modulo 23
2) Propose a theorem
I found the answer:
1) It is all 1
2) The theorem is as following:
(a^(n-1) modulo n) = 1; where n is prime;
n >= 3 and a > 0
There is not proof required for homework;
But I want to prove the theorem; but I am stuck
since induction does not seem to work due to
variance nature of n; any hint. Thanks.
KingGeorge is needed. Thanks. Regards.

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it has possibly to do with relatively prime stuff

if p and q are prime, then p mod q = p
p^(q-1) mod q
p^(q) p^(-1) mod q
p^q mod q = 1, proof it?

king george might be more elegant, i agree :)

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