(all expressions are Mod q)
Consider the q-1 numbers p, 2p, 3p, 4p, 5p,...,(q-1)p.
All these numbers are different and nonzero. If ap = bp and p and q don't have divisors in common then a = b. So, a - b must be zero or a multiple of q, which means that all the q - 1 multiples of p are different and nonzero.
Since there are only q-1 nonzero numbers Mod q:
1, 2, 3, ... q-1,
this means that the numbers
p, 2p, 3p, 4p, 5p,...,(q-1)p
are just the numbers
1, 2, 3,... q-1
but in some different order.
This means that:
We can write:
And it follows that:
p^(q-1) = 1
You can simplify a but more by using that 17 = 3
So, you get 3^2 = 9 = 2 as the answer.
Answer this Question
*** Discrete Math *** - I have solved parts of the question, but I want to know ...
Geography - I just want to make sure that I have the correct answers for 2 ...
Algebra II-Please check fpr explanation - I have a question concerning this ...
*** Discrete Math *** - I would like to know if my answers are correct. I also ...
Organic chemisty(Please check) - When drawing a kekule structure for CH3CH2OH(...
philosophy - I have to write a 1 page paper "presenting what i believe the world...
Physics - I had a two part question in which I'm fairly sure I did the first ...
Algebra - Consider the equation 5x + 2y = 30. Part 1: On your own paper, graph ...
algebra - Consider the equation 7x + 3y = 42. Part 1: On your own paper, graph ...
physics(check my answer) - A 60.0 kg person bends his knees and then jumps ...