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

**sbacon1991** · January 13th 2012, 09:47 AM

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

**princeps** · January 13th 2012, 10:02 AM

Originally Posted by sbacon1991

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

$a^{\phi(m)} \equiv 1 \pmod m$ ,so you have that :

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

**sbacon1991** · January 13th 2012, 10:07 AM

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

**princeps** · January 13th 2012, 10:10 AM

Originally Posted by sbacon1991

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

Euler's Theorem

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

LinkBack

Thread Tools

Display

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

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

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

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

Similar Math Help Forum Discussions

Using Extended Euclidean Alogirthm to compute Chinese Remainder Theorem

[SOLVED] Compute the remainder: Fermat's Little Theorem

Compute the remainder: Fermat's Little Theorem

Extended Divided Difference

Extended Fermat's Last Theorem

Search Tags