The Erdős-Turán conjecture states that if the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic progressions.

formulation date | 1936 (90 years ago) formulators | Paul Erdős | Paul Turán status | open

prize offered for solution | Erdős offered a $3, 000 prize for a proof. | The prize was increased to $5, 000 in 2008.

mathematical conjectures | prize mathematics problems | unsolved mathematics problems