Calculate 15843(mod11)
My solution
Fermat's little theorem
Since 15≡4(mod11) and according Fermat's Little Theorem
410≡1(mod11),
we shall have
15843≡4843≡4840×43≡(410)84×43≡43≡64≡9(mod11)
Is this correct?
Answer
Is this correct?
It is.
Fermat's little theorem is indeed one very useful tool to finding the answer, and in case you have any doubt whether you got that part right, you can verify that:
410=1048576=11×95325+1≡1(mod11)
The rest is just using the properties of modular arithmetic to replace some terms by congruent but simpler terms. Done explicitely, and correctly, so I see no reason to doubt the result.
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