TinyMistral-248M-v2

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• TITLE: Dirichlet density QUESTION [5 upvotes]: How to solve the following exercise: Let $q$ be prime. Show that the set of primes p for which $p \equiv 1\pmod q$ and $2^{(p-1)/q} \equiv 1 \pmod p$ has Dirichlet density $\dfrac{1}{q(q-1)}$. I want to show that $X^q-2$ (mod $p$) has a solution and $q$ divides $p-1$ , these two conditions are simultaneonusly satisfied iff p splits completely in $\Bbb{Q}(\zeta_q,2^{\frac{1}{q}})$. $\zeta_q $ is primitive $q^{th}$ root of unity. If this is proved the I can conclude the result by Chebotarev density theorem. REPLY [2 votes]:Copy
• An emerging clinical approach to treat substance abuse disorders involves a form of cognitive-behavioral therapy whereby addicts learn to reduce their reactivity to drug-paired stimuli through cue-exposure or extinction training. It is, however,Copy
• \begin{document} \begin{frontmatter} \author{Mahouton Norbert Hounkonnou\corref{cor1}${}^1$} \cortext[cor1]{[email protected]} \author{Sama Arjika\corref{cor2}${}^1$} \cortext[cor2]{[email protected]} \author{ Won Sang Chung\corref{cor3}${}^2$ } \cortext[cor3]{[email protected]} \title{\bf New families of $q$ and $(q;p)-$Hermite polynomials } \address{${}^1$International Chair of Mathematical Physics and Applications \\ (ICMPA-UNESCO Chair), University of Abomey-Calavi,\\ 072 B. P.: 50 Cotonou, Republic of Benin,\\ ${}^2$Department of Physics and Research Institute of Natural Science, \\ College of Natural Science, \\ Gyeongsang National University, Jinju 660-701, Korea } \begin{abstract} In this paper, we construct a new family of $q-$Hermite polynomials denoted by $H_n(x,s|q).$ Main properties and relations are established andCopy