Continuous plus zero integral around every triangle forces holomorphicity.Suggest a slogan
Let \(\Omega\subseteq\CC\) be open and let \(f\colon\Omega\to\CC\) be continuous. If \(\int_{\partial T}f(z)\dz=0\) for every closed triangle \(T\subseteq\Omega\), then \(f\) is holomorphic on \(\Omega\).