def lehman_simple(n): # Find a nontrivial factor m of n; if n prime then m==n # Pre: n > 1 # Post: return m; m > 1, n % m == 0; m == n only if n is prime n_1_3 = int(ceil(pow(n, 1.0/3.0))) n_1_6 = pow(n, 1.0/6.0) # 1. Trial division ub_d = max(n_1_3, 19) # Ensures n > 21 in step 2. for d in range(2,ub_d+1): if n % d == 0: return d # 2. Loop for k in range(1,n_1_3+1): lb = int(ceil(2*sqrt(k*n))) ub = int(floor(2*sqrt(k*n) + n_1_6/(4*sqrt(k)))) for a in range(lb, ub+1): delta = a*a - 4*k*n b = int(floor(sqrt(delta))) if b*b == delta: return GCD.gcd(a+b, n) return n
def gcd(a): gcd = a[0] for x in a: gcd = GCD.gcd(x, gcd) return gcd
def DecimalExpansion(n):
for x in range(1, 2000):
if((10**x) % n == 1 and GCD.gcd(10, n)):
return x
return -1
