What constitutes proof?
By assuming that you can factor in the same time complexity as it takes to generate an RSA sized semiprime
(The time complexity of multiplying two numbers together)
Look up Newton root finding. It’s how the newer square root method works and can be used to calculate other methods provided you have a way of refining your estimate.
Root finding factorization?
Closer than you’d think to solve.
Dividing by 2 until odd (tree) is also used in Miller-Rabin to decompose a value into powers of 2 and a remainder.
Philippians 1:8-11