Least Residue!

**dancer17** · March 5th 2008, 06:43 PM

Can someone pls help me with this question????

Find the least residue of 789^3217 modulo the prime 1607.

**PaulRS** · March 6th 2008, 02:01 AM

Remember Fermat's Little Theorem, if $p$ is prime and $a$ a natural number then $a^p\equiv{a}(\bmod.{p})$

For our case: $789^{1607}\equiv{789}(\bmod.{1607})$

Squaring: $789^{3214}\equiv{789^2}(\bmod.{1607})$

And: $789^{3217}\equiv{789^5}\equiv{772}(\bmod.{1607})$

**dancer17** · March 6th 2008, 10:15 AM

HEy Thanks!

I'm just not sure how you got the 789^5.

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Least Residue!

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