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Zp question


yda

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Firstly, this isn't true unless p is a prime, if it is a prime then say so.

 

The answer as always follows from the hint: all you know (if p is a prime), is that a and p are coprime. Hence all you can do is use the single result at your disposal, ie Euclid's Algorithm.

 

Let us know where that gets you

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What does Euclid tell us? That given a and p coprime, there are integers x and y with

 

ax+py=1

 

 

can you now see how to express b as "a" times something plus something congruent to zero mod p?

 

Note that if all we require is that a is not zero then p must be a prime, but it suffices just for a and p to be coprime.

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