0000000000014079

AUTHOR

Martin Helm

showing 2 related works from this author

On the Distribution ofB3-Sequences

1996

Abstract An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withaj∈Aanda1⩽a2⩽a3are distinct. LetA(n) be the number of positive elements ⩽ninA. P. Erdos conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)∼αn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.

Discrete mathematicsCombinatoricsSequenceInfinite setAlgebra and Number TheoryDistribution (number theory)Natural numberMathematicsJournal of Number Theory
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Some remarks on the Erdős-Turán conjecture

1993

CombinatoricsAlgebra and Number TheoryConjectureElliott–Halberstam conjectureabc conjectureBeal's conjectureErdős–Straus conjectureErdős–Gyárfás conjectureLonely runner conjectureMathematicsCollatz conjectureActa Arithmetica
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