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

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

2007-03-15

arxiv.org/abs/math/0703467v1

Mathematics

Number Theory

Scientific paper

We 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.

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