The board / number theory / #946
Erdős Problem #946
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There are infinitely many \(n\) such that \(τ(n) = τ(n+1)\). Proved in [He84]. Here τ is the divisor counting function, which is `σ 0` in mathlib.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/946.Prizenone
Topicsnumber theory, divisors
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/946
Attempts
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