Determine all functions $f(n)$ such that $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}$ then $\frac{1}{f(a)} + \frac{1}{f(b)} = \frac{1}{f(c)}$.
129052
Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
78471
Closure of $\{\frac{1}{n}\}:=M$
86128
Find all functions $ f : \Bbb R \to \Bbb R$ which satisfy $f(x)f(y) = f(x + y) + xy$ for all $x, y ∈ \Bbb R$.
134195
Holomorphic function $f:B(0,1) \to B(1,4)$ with $f(0)=3$ and $f(\frac{1}{2})=1$
9587
If $f(t) = 1+ \frac{1}{2} +\frac{1}{3}+....+\frac{1}{t}$, find $\sum^n_{r=1} (2r+1)f(r)$ in terms of $f(n)$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
55485
Recursive Function - $f(n)=f(an)+f(bn)+n$
106748
Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
99894
Does there exists an entire function $f$ such that $f(0)=1$ and $|f(z)|\leq \frac{1}{|z|} $ for all $|z|\geq 5$?
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$