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Let $f:\mathbb{R}\to \mathbb{R}$ be such that $f(x+h)-f(x)$ is continous for every $h>0$. Is it true that \[f=g+h\] for some continuous $g$ and additive $h$ (i.e. $h(x+y)=h(x)+h(y)$)?
A conjecture of Erdős from the early 1950s. Answered in the affirmative by de Bruijn [dB51].

See also [908].