Erdős Problem #907
PROVED LEANdatabase updated 2026-04-07
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(f:\mathbb{R}\to \mathbb{R}\) be such that \(f(x+h)-f(x)\) is continuous 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].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/907.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/907
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.