def main(verbose=False):
product = 13082761331670030
factors = prime_factors(product)
candidate_lists = []
for factor in factors:
candidate_lists.append([(factor, root)
for root in find_cube_roots(factor)])
result = list(i_product(*candidate_lists))
coprime_units = {}
for factor in factors:
_, multiplier = extended_euclid(factor, product / factor)
coprime_units[factor] = multiplier * (product / factor)
vals = []
for pairing in result:
count = 0
for prime, residue in pairing:
count += residue * coprime_units[prime]
count = count % product
vals.append(count)
return sum(vals) - 1 # 1 is in there as (1,1,...,1)
def unit_a_zero_b(a, b):
_, multiplier = extended_euclid(a, b)
return (multiplier * b) % (a * b)