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#include <iostream>
#include <optional>
#include <tuple>
std::tuple<int, int, int> extended_gcd(int a, int b) {
if (b == 0) return {a, 1, 0};
auto [g, x, y] = extended_gcd(b, a%b);
return {g, y, x - y*(a/b)};
}
template<int N>
class Zmod {
public:
int value;
Zmod(int z) : value{(z%N + N) % N} {}
int toint() const { return value; }
Zmod operator+(const Zmod& z) const { return value + z.value; }
Zmod operator-(const Zmod& z) const { return value - z.value; }
Zmod operator*(const Zmod& z) const { return value * z.value; }
std::optional<Zmod> inverse() const {
auto [g, a, _] = extended_gcd(value, N);
return g == 1 ? Zmod(a) : std::optional<Zmod>{};
}
std::optional<Zmod> operator/(const Zmod& d) const {
auto i = d.inverse();
return i ? (*this) * i.value() : i;
}
std::optional<Zmod> operator/=(const Zmod& d) {
auto q = *this / d;
return q ? (*this = q.value()) : q;
}
};
int main() {
Zmod<57> x(34);
Zmod<57> y(11);
std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl;
if (auto inv = y.inverse(); inv)
std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl;
else
std::cout << "11 is not invertible in Z/57Z" << std::endl;
// The following line gives a run-time exception
// Zmod<0> z(157);
return 0;
}
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