def find_solution():
res = []
for number in xrange(2, 10000):
factors = factorize(number)
d1 = (sum(make_divisors(factors)) - number)
factors = factorize(d1)
d2 = (sum(make_divisors(factors)) - d1)
if d2 == number and d1 != number:
res.append(number)
return sum(res)
def main():
n = int(input('Введите n = '))
k = int(input('Введите k = '))
iters = int(input('Введите l = '))
factors = factorize(n, fermat, k, iters)
print('\n'.join(map(str, factors.items())))
def p29():
"""
To factorize (A^B), factorize A then multiply the prime powers by B. Store
the factorizations and check for uniqueness
"""
primeList = []
prime = gen_primes()
p = next(prime)
while (len(primeList) < 100):
primeList.append(p)
p = next(prime)
factorSet = []
for base in range(2, 101):
for power in range(2, 101):
factors = factorize(base, primeList)
for i in range(len(factors)):
factors[i] *= power
unique = 1
for i in range(len(factorSet)):
match = 1
for j in range(len(factorSet[i])):
if factorSet[i][j] != factors[j]:
match = 0
break
if (match):
unique = 0
break
if (unique):
factorSet.append(factors)
print(len(factorSet))
def main():
if len(argv) == 1:
n = int(input('Введите n = '))
c = int(input('Введите с = ')) % n
assert 1 < c < n, 'c должно быть 1 < c < n'
elif len(argv) == 2:
n = int(argv[1])
c = int(input('Введите с = ')) % n
else:
n = int(argv[1])
c = int(argv[2]) % n
assert 1 < c < n, 'c должно быть 1 < c < n'
factors = factorize(n, p_pollard, c)
print('\n'.join(map(str, factors.items())))
def find_solution():
abundant_numbers = []
res = 1
for i in xrange(2, 28124):
found = False
if sum(make_divisors(factorize(i))) > 2*i:
abundant_numbers.append(i)
for number in abundant_numbers:
if i - number in abundant_numbers:
found = True
break
if 2*number > i:
break
if not found:
res += i
return res
def toneli_shanks(a, p):
# find z such as Legendre symbol (z/p) == -1
z = get_non_quad(p)
q = p - 1
s, q = factorize(q) #(p-1)=2^n*k
c = fast(z, q, p)
r = fast(a, (q + 1) // 2, p)
t = fast(a, q, p)
m = s
while t % p != 1:
i = 1 #Find the least i such as t^2^imodp=1modp
while fast(t, 2**i,
p) != 1: #if i!=0 then increase until c^2^(m-i-1) = 1modp
i += 1
b = fast(c, 2**(m - i - 1), p)
r = r * b % p
t = t * b * b % p
c = b * b % p
m = i
return r, p - r #solutions
def test_8(self):
self.assertEqual(prime.factorize(8), [2,2,2])
def test_2(self):
self.assertEqual(prime.factorize(2), [2])
def test_2342623178(self):
self.assertEqual(prime.factorize(2342623178), [2,7,1237,135271])
def test_4126264356(self):
self.assertEqual(prime.factorize(4126264356), [2,2,3,59,5828057])
def test_34503489(self):
self.assertEqual(prime.factorize(34503489), [3,3,3,3,17,25057])
def test_empty(self):
self.assertEqual(prime.factorize(1), [])
def prime_time(n):
print('Factorizing', n)
start = time.clock()
print(prime.factorize(n))
stop = time.clock() - start
print('Factorization took {:.2f} seconds.'.format(stop))
def test_100(self):
self.assertEqual(prime.factorize(100), [2,2,5,5])
def test_3(self):
self.assertEqual(prime.factorize(3), [3])
def test_7(self):
self.assertEqual(prime.factorize(7), [7])
def test_6(self):
self.assertEqual(prime.factorize(6), [2,3])
def test_5(self):
self.assertEqual(prime.factorize(5), [5])
def test_4(self):
self.assertEqual(prime.factorize(4), [2,2])
def number_of_divisors_less(number, limit):
factors = factorize(number)
if 2**len(factors) < limit:
return True
return len(make_divisors(factors)) < limit
def test_9(self):
self.assertEqual(prime.factorize(9), [3,3])