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

Goutam Pal

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

Goutam Pal

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Abstract

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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Goutam Pal. 2007-03-15. On sequences of positive integers having no $p$ terms in arithmetic progression. https://arxiv.org/abs/math/0703467

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