Expert · Number theory · 240 of 264
Modular inverse
Find x between 0 and m - 1 with a * x mod m = 1, using the extended Euclidean algorithm. If it does not exist, print none.
Input: a and m on one line. Output: x or none
Examples
Input
3 11
Output
4
Input
10 17
Output
12
Input
6 9
Output
none
One more test checks other inputs when you press Check.
Stuck? The idea behind number theory
Whole-number tricks: n % d == 0 means d divides n; test divisors only up to the square root; the sieve of Eratosthenes finds every prime up to n at once.
pow(a, b, m) works out a to the power b, modulo m, quickly, even when the power is huge.
n = 50
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n ** 0.5) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
print(sum(is_prime))Watch for: Testing every number up to n one by one is too slow for big inputs: the hidden tests notice.