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## Homework Statement

Let f and g be two holomorphic functions in a connected open set D of the plane which have no zeros in D; if there is a sequence a_{n}of points such that lim a

_{n}= a and a

_{n}does not equal a for all n, and if

f'(a

_{n})/f(a

_{n})=g'(a

_{n})/g(a

_{n})

show that there is a constant c such that f=cg in D.

## Homework Equations

If f is identically zero at a point in a connected open set, then f is identically zero on the whole set.## The Attempt at a Solution

I have shown that (f/g)'(a) = 0, but I don't see how that would imply that the derivative is identically zero at that point.
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