# Thread: Using Extended Fermat Little Theorem ﬁnd t remainder when 11^1001 is divided by 12

1. ## Using Extended Fermat Little Theorem ﬁnd t remainder when 11^1001 is divided by 12

Using the Extended Fermat Little Theorem ﬁnd the remainder when 11
1001
is
divided by 12.

2. ## Re: Using Extended Fermat Little Theorem ﬁnd t remainder when 11^1001 is divided by

Originally Posted by sbacon1991
Using the Extended Fermat Little Theorem ﬁnd the remainder when 11
1001
is
divided by 12.
$\displaystyle a^{\phi(m)} \equiv 1 \pmod m$ ,so you have that :

$\displaystyle 11^4 \equiv 1 \pmod {12} \Rightarrow (11^4)^{250} \equiv 1 \pmod {12} \Rightarrow 11 \cdot 11^{1000} \equiv 11 \pmod {12}$

3. ## Re: Using Extended Fermat Little Theorem ﬁnd t remainder when 11^1001 is divided by

its surely only true is m is prime and 12 is not prime?

4. ## Re: Using Extended Fermat Little Theorem ﬁnd t remainder when 11^1001 is divided by

Originally Posted by sbacon1991
its surely only true is m is prime and 12 is not prime?

Euler's Theorem