This question i am having trouble with.
Let n be an odd positive integer. Prove there is a one-to-one correspondence
between the factorisation of n into the form n = ab where a >=b >= 1, and
representations of the form s ^2-t^2where s, t ∈ Z satisfy s > t >=0.
I have set n=ab=s²-t²=(s+t)(s-t)
and solved for s and t, i have then showed by use of congruences that the sum and differenc of two odd integers is even, and thus s and t are even,but i am still having trouble fully understanding how exactly and why there is a one to one corespondance. If anyone understands this concept properly i would like some help as i am not fully grasping it.