# Revision history [back]

If you want to factor N=8979 then trial division is your best choice (here in a very naive version)

def factor_via_trial_division(N):
fac = []
i = 2
while i*i < N:
while N % i == 0:
fac.append(i)
N //= i
i += 1
return fac + [N]


You got

sage: %time factor_via_trial_division(8979)
CPU times: user 70 µs, sys: 3 µs, total: 73 µs
Wall time: 84.2 µs
[3, 41, 73]


Multivariate diophantine systems of degree > 1 are known to be complicated, see https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem. In particular, it has been proven that there does not exist an algorithm that takes as input a diophantine system and outputs one of its solution if it exists. Because of this, it is hard to believe that building a complicated diophantine system will help in any way to factor.