1. Fermat's Little Theorem

Let p be a prime number, not 2 or 5.

Show that $10^{p-1} \equiv 1 \pmod p \quad \quad$

I can show the workings for some primes i.e 3,7 but how do i show for all primes except 2 and 5?

thanks

2. Originally Posted by charikaar
Let p be a prime number, not 2 or 5.

Show that $10^{p-1} \equiv 1 \pmod p \quad \quad$

I can show the workings for some primes i.e 3,7 but how do i show for all primes except 2 and 5?

thanks
Let $p$ be a prime, then $\left(10,p\right)\ne1$ if and only if $p=2,5$ (this is easy to deduce). So...apply the name of this thread.