Multiplicative Functions on Arithmetic Progressions
نویسندگان
چکیده
منابع مشابه
On rainbow 4-term arithmetic progressions
{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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Let d > 4 and c ∈ (−d, d) be relatively prime integers, and let r(d) be the product of all distinct prime divisors of d. We show that for any sufficiently large integer n (in particular n > 24310 suffices for 4 6 d 6 36) the least positive integer m with 2r(d)k(dk− c) (k = 1, . . . , n) pairwise distinct modulo m is just the first prime p ≡ c (mod d) with p > (2dn − c)/(d − 1). We also conjectu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.2307/2048277