let n=1105, so n-1=2^4(69) Compute the values of
2^69(mod1105), 2^2*69(mod 1105), 2^4*69(mod1105), 2^8*69(mod1105),
Use the Rabin Miller test to conclue that n is composite....
Where do I begin and how?
In the Rabin-Miller test for the (pseudo) primality of $\displaystyle 1105$ we have $\displaystyle s=4$ and $\displaystyle d=69$
So $\displaystyle a$ is a witness to the primallity of $\displaystyle 1105$ if:
$\displaystyle
a^d \not \equiv 1 \mod 1105
$
and
$\displaystyle
a^{2^r.d} \not \equiv -1 \mod 1105; \forall \ r \in \{0,\ ..., \ s-1\}
$
So if you compute the values asked for and the first is not congruent to $\displaystyle \pm 1 \mod 1105$ and the others are not congruent to $\displaystyle -1 \mod 1105$, then $\displaystyle 2$ is a witness to the compositness of $\displaystyle 1105$. (In fact if the conditions hold then 1105 is certainly composite, if they fail 1105 is probably prime)
RonL