Science:Math Exam Resources/Courses/MATH312/December 2012/Question 02 (c)/Hint 1

Recall that 7 passes Miller's test if

$\displaystyle 7^{d}\equiv 1\mod {25}$

or the following holds for some r

$\displaystyle 7^{2^{r}d}\equiv -1\mod {25}$

where $\displaystyle 25-1=24=2^{s}d$ for $s=3$ and $d=3$, and $\displaystyle 0\leq r\leq s-1$.

If 7 passes the test, then 25 is a probable prime. If it fails the test, then the number is not prime.