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( 1 point ) The Miller - Rabin primality test is based around the following observation. If p is prime and x 2 - =

(1 point) The Miller-Rabin primality test is based around the following observation.
If p is prime and x2-=1,modp then x-=+-1,modp.
Note that x-=-1,modp and x-=p-1,modp mean the same thing.
We will use the Miller-Rabin test to test n=2905 for primality. To do this we will closely examine
an-1modn for various integers a.
First we divide out all of the 2's from n-1.
We can write n-1=2ur where
u=
is maximal, and
r=
Now we randomly select some ainZn, such as a=2823.
Initially we compute
ar-=,modn.
If this number is 1 then the test is inconclusive and another a is selected (up until the number of
a's determined by the security level).
Otherwise we compute the list of values a2r,a4r,dots,a2ir,dots,a2ur. Note a2ur=an-1.
Please enter this list for n=2905 and a=2823 in comma separated format.
When the list is computed one of a few things could happen.
The value 1 never occurs on the list.
The value -1-=p-1,modp occurs on the list, immediately followed by 1.
The value 1 occurs in the list, but preceded by -1.
Which one of these possibilities holds in our case (enter the number)?
What conclusion should we draw from what we have done?
n is prime.
n is composite.
The test is inconclusive.
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