Hello everyone, this is my first post and might be trivial.

After some calculations, i come up with the following equality:

2F1(1,1/n,1+1/n,a c)==2F1(1,1/n,1+1/n,b c) (1)

where, 2F1 is Gauss' hypergeometric function, n,c real positive quantities.

Obviously, the equality holds when a==b (2). My problem is that i want to show that (2) is not only sufficient but also necessary, i.e. (1) holds only when (2) holds.

Any ideas?

TIA