On generalised arithmetic and geometric progressions
نویسندگان
چکیده
منابع مشابه
On the intersection of infinite geometric and arithmetic progressions
We prove that the intersection G ∩A of an infinite geometric progression G = u, uq, uq2, uq3, . . . , where u > 0 and q > 1 are real numbers, and an infinite arithmetic progression A contains at most 3 elements except for two kinds of ratios q. The first exception occurs for q = r1/d , where r > 1 is a rational number and d ∈ N. Then this intersection can be of any cardinality s ∈ N or infinite...
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{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1982
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-40-3-255-262