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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]:
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# Training
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This model was trained on two datasets, shown in this model page.
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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]:
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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,
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# Training
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This model was trained on two datasets, shown in this model page.
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