Using the Extended Fermat Little Theorem ﬁnd the remainder when 11 1001 is divided by 12.
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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 : $\displaystyle 11^4 \equiv 1 \pmod {12} \Rightarrow (11^4)^{250} \equiv 1 \pmod {12} \Rightarrow 11 \cdot 11^{1000} \equiv 11 \pmod {12}$
its surely only true is m is prime and 12 is not prime?
Originally Posted by sbacon1991 its surely only true is m is prime and 12 is not prime? Euler's Theorem
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