A Consideration on Verification and Extension of Fermat's Factorization

There are some efficient brute force algorithm for factorization. Fermat's factorization is one of the way of brute force attack. Fermat's method works best when there is factor near the square-root. This paper shows that why Fermat's method is effective and verify that there are only one answer. Because there are only one answer, we can start Fermat's factorization anywhere. Also, we convert from factorization to finding square number.