On sequences of positive integers having no $p$ terms in arithmetic progression

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125765We use topological ideas to show that, assuming the conjecture of Erd\"(o)s on subsets of positive integers having no $p$ terms in arithmetic progression (A. P.), there must exist a subset $M_p$ of positive integers with no $p$ terms in A. P. with the property that among all such subsets, $M_p$ maximizes the sum of the reciprocals of its elements.Number TheoryOn sequences of positive integers having no $p$ terms in arithmetic progressiontext