Question

Show that if n is prime and b is a positive integer with $n\times b$, then n passes Miller’s test to the base b.

Short answer

answer is missing in file

Step-by-step solution

Step: 1

Similarly let n=1105

1105=5X13X17

$\begin{array}{r}{p}_1=5\\ P_2=13\\ P_3=17\\ p_1-1=4\\ p_2-1=12\\ p_3-1=16\\ n-1=1105-1\\ n-1=1104\end{array}$

n-1 is divisible by $p_1-1$.

Step: 2

Similarly, n-1 is also divisible by $p_2-1$and $p_3-1$

So, n=1105 is a Carmichael number.