On a problem of Erdos and Moser

Bollobas, Bela; Scott, Alex
We prove that for any $\epsilon$ {\textgreater} 0 there is k($\epsilon$) such that for any prime p and any integer c there exist k ≦ k($\epsilon$) pairwise distinct integers xi with 1 ≦ xi ≦ p$\epsilon$, i = 1,...,k, and such that ∑i=1k1/xi ≡ c (mod p). This gives a positive answer to a question of Erdos and Graham.
Research areas:
Year:
2016
Type of Publication:
Article
Keywords:
Blocks of consecutive integers; Diophantine equations; Runge'; s method
Journal:
Periodica Mathematica Hungarica
Volume:
72
Number:
1
Pages:
23-28
ISSN:
1588-2829
DOI:
10.1007/s10998-015-0098-8
Hits: 3635

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