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On consecutive sums in sequences

✍ Scribed by N. Hegyvári

Publisher: Akadmiai Kiad
Year: 1986
Tongue: English
Weight: 279 KB
Volume: 48
Category: Article
ISSN: 1588-2632
DOI: 10.1007/bf01949064

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For k>2 and r 2, let G(k, r) denote the smallest positive integer g such that every increasing sequence of g integers [a 1 , a 2 , ..., a g ] with gaps a j+1 &a j # [1, ..., r], 1 j g&1 contains a k-term arithmetic progression. Brown and Hare proved that G(k, 2)>-(k&1)Â2 ( 43 ) (k&1)Â2 and that G(k,