#include using namespace std; using ll = long long; //ax + by = gcd(a,b) template T extgcd(T a, T b, T& x, T& y) { if (b) { T d = extgcd(b, a % b, y, x); y -= a / b * x; return d; } else { x = 1; y = 0; return a; } } //modular inverse of a mod m template T modinv(T a, T m) { T x, y; T d = extgcd(a, m, x, y); if (d != 1) return -1; x %= m; if (x < 0) x += m; return x; } //res = r (mod m) template T garner(vector r, vector m) { assert(r.size() == m.size()); int N = (int)r.size(); T prod = 1, res = r[0] % m[0]; for (int i = 1; i < N; i++) { prod *= m[i - 1]; T tmp = ((r[i] - res) * modinv(prod, m[i])) % m[i]; if (tmp < 0) tmp += m[i]; res += tmp * prod; } return res; } template vector> prime_factorize(T n) { vector> ret; for (T i = 2; i * i <= n; i++) { if (n % i == 0) { int num = 0; while (n % i == 0) { num++; n /= i; } ret.push_back({i, num}); } } if (n != 1) ret.push_back({n, 1}); return ret; } template T pow(T x, int n) { T res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } int main() { int N; cin >> N; vector X(N), Y(N); for (int i = 0; i < N; i++) { cin >> X[i] >> Y[i]; } map> mods; for (int i = 0; i < N; i++) { auto V = prime_factorize(Y[i]); for (auto& [m, power] : V) { ll rem = X[i] % pow(m, power); if (!mods.count(m)) { mods[m] = {power, rem}; } else { auto& [power_bef, rem_bef] = mods[m]; if ((rem - rem_bef) % pow(m, min(power, power_bef)) != 0) { cout << -1 << endl; exit(0); } else { if (power_bef < power) { power_bef = power; rem_bef = rem; } } } } } vector m, r; for (auto& [mod, p] : mods) { m.emplace_back(pow(mod, p.first)); r.emplace_back(p.second); } cout << garner(r, m) << endl; }