The board / number theory / #250
Erdős Problem #250
PROVED LEANdatabase updated 2026-08-23
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).
Is \[ \sum_{n=1}^\infty \frac{\sigma(n)}{2^n} \] irrational? Here \(\sigma(n)\) is the sum of divisors function. The answer is yes, as shown by Nesterenko [Ne96]. [Ne96] Nesterenko, Yu V., _Modular functions and transcendence questions_, Mat. Sb. 187 *9* (1996), 1319--1348.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/250.Prizenone
Topicsnumber theory, irrationality
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA066766
Original pageerdosproblems.com/250
Attempts
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