# Number theory help

1. Mar 6, 2006

### buzzmath

I'm trying to show that 25 is a strong pseudoprime to the base 7 using millers test. Is there a better way to solve this than just brute force?
Thanks

2. Mar 6, 2006

### CarlB

I'm not sure of the notation. I assume that you need to compute

$$7^{25}\;\;\textrm{mod}\;(25).$$

The way to do is to avoid letting the power get all out of control. Consider:

7*7 = 49 = 24 = -1 mod (25)

so
7*7*7*7 = 1 mod (25).

so what is 7^{24}?

Carl