restart.'s blog

Primitive root modulo n
By restart., history, 11 years ago, In English

Given a number n as input how to find the (all the primitive roots of n) % n if n is prime. please give me some hint how can i calculate the primitive roots.. TIA.

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11 years ago, hide # |
 
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  1. Find the smallest one. Let's call it g.
  2. gi will be a primitive root if and only if i and φ(n) are coprime.
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    11 years ago, hide # ^ |
     
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    in this spoj problem how can i find the (product all the primitive roots of n) % n without generating all the primitive roots of n ? any hint please...

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      11 years ago, hide # ^ |
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      For your question: sum of numbers relatively prime and less than N is Nφ(N) / 2. (Because if gcd(x, N) = 1 then gcd(N - x, N) = 1). But since for any primitive root g, gi is primitive root if and only if gcd(i, φ(N)) = 1. So their product will be gφ(φ (N)) * φ (N) / 2 which is ( - 1)φ(φ(n)) since g is primitive root. For you particular case it is -1.

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