def shanks(p, alpha, beta):
m = int(math.ceil(math.sqrt(p - 1)))
inv_alpha, r, t = ex3.solve_bezout(alpha, p, 1)
l1 = [0]*m
l2 = [0]*m
l1[0] = 0, alpha
l1[1] = 1, pow(alpha, m)%p
l2[0] = 0, beta
l2[1] = 1, (beta*(inv_alpha))%p
for j in xrange(2, m):
l1[j] = (j, (l1[1][1]*l1[j - 1][1])%p)
l2[j] = (j, (l2[j - 1][1]*inv_alpha)%p)
for i in l1:
for j in l2:
if i[1] == j[1]:
return m*i[0] + j[0]
t = 1
old_t = 0
r = b
old_r = a
while not r == 0:
q = old_r//r
(old_r, r) = (r, old_r - q*r)
(old_s, s) = (s, old_s - q*s)
(old_t, t) = (t, old_t - q*t)
return old_r
def brute_force_eq(a, b, c, it):
for i in xrange(it):
for j in xrange(it):
if (a*i - b*j) == c:
return (i, -1*j)
if (a*i - b*j) < 0:
break
if __name__ == "__main__":
print mdc(8765, 23485)
print brute_force_eq(65537, 3511, 1, 10000000)
print brute_force_eq(65537, 3511, 17, 10000000)
print ex3.solve_bezout(17, 101, 1)
print ex3.solve_bezout(357, 1234, 1)
print ex3.solve_bezout(3125, 9987, 1)
