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bool isPrimitive(ll g, ll n, ll phi, map<ll, int> phiFacs) {
if (g == 1) return n == 2;
for (auto& f : phiFacs)
if (1 == powMod(g, phi / f.first, n)) return false;
return true;
}
bool isPrimitive(ll g, ll n) {
ll phin = phi(n); //isPrime(n) => phi(n) = n - 1
map<ll, int> phiFacs;
factor(phin, phiFacs);
return isPrimitive(g, n, phin, phiFacs);
}
ll findPrimitive(ll n) {
ll phin = phi(n); //isPrime(n) => phi(n) = n - 1
map<ll, int> phiFacs;
factor(phin, phiFacs);
//auch zufällige Reihenfolge möglich!
for (ll res = 1; res < n; res++)
if (isPrimitive(res, n, phin, phiFacs)) return res;
return -1;
}
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