是否有一种算法可以计算x模y的乘法阶数(对于y<1000),而不需要BigInteger类型?

Wikipedia 有关详细信息,还有以下示例代码:

Bignum modpow(Bignum base, Bignum exponent, Bignum modulus) {

    Bignum result = 1;

    while (exponent > 0) {
        if ((exponent & 1) == 1) {
            // multiply in this bit's contribution while using modulus to keep result small
            result = (result * base) % modulus;
        }
        // move to the next bit of the exponent, square (and mod) the base accordingly
        exponent >>= 1;
        base = (base * base) % modulus;
    }

    return result;
}

为什么要指数化?你就不能乘模吗 n 在循环中?

(defun multiplicative-order (a n)
  (if (> (gcd a n) 1)
      0
      (do ((order 1 (+ order 1))
           (mod-exp (mod a n) (mod (* mod-exp a) n)))
          ((= mod-exp 1) order))))

或者,在ptheudo(sic)代码中:

def multiplicative_order (a, n) :
    if gcd (a, n) > 1 :
        return 0
      else:
        order = 1
        mod_exp = a mod n
        while mod_exp != 1 :
            order += 1
            mod_exp = (mod_exp * a) mod n
        return order