I am struggling to understand the following passage from my number theory book, i'm not sure i like his choice of language however it is the only book i can get a copy of for now. That being said I was wondering if someone could see if my understanding of this passage is OK. Would be much appreciated !
"Fermat's factorization scheme has at its heart the observation that the search for factors of an odd integer n (because powers of 2 are easily recognizable and may be removed at the outset, there is no loss in assuming that n is odd) is equivalent to obtaining integral solution x and y of the equation $n = x^2 - y^2$.
Does this passage mean that we assume that any integer $n$ that we are dealing with has already had the prime factor $2^k$ removed and therefore we can assume that the number N and the remaining prime factors are odd? This in turn enables us to use the fact that any odd integer can be represented as the difference of two squares.