Open Research Index

Erdős problem #266: the Kovač–Tao disproof of Stolarsky's conjecture

Ben Keene

Palomar Registrypalomar/PALOMAR-2026-08-20-000008Oct 12, 2026math.NTscore 0

A Lean 4 formalization, against Mathlib, of the Kovač–Tao resolution of Erdős problem #266 (a conjecture of Stolarsky): it is not true that every sequence of positive integers with convergent reciprocal sum admits an integer shift t >= 1 making the shifted Ahmes series irrational. The stronger construction is also formalized: a strictly increasing sequence of positive integers whose shifted series has a rational sum for every admissible rational shift.

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