Artificial intelligent assistant

potence

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potence
▪ I. potence1 (ˈpəʊtəns) [a. OF. potence, ad. L. potentia power, f. potent-em, pres. pple. of posse to be powerful or able: see -ence.] 1. Power, ability, strength; = potency 1.1413 Pilgr. Sowle (Caxton 1483) iv. xxvi. 72 That he ne may it knowen as in potence that is kyndely power. 1596 Dalrymple t... Oxford English Dictionary
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Félix Poutré
Pied-du-Courant Prison by allegedly feigning madness, Poutré published a pamphlet giving an account of his experiences, under the title Échappé de la potence wikipedia.org
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pottance
pottance variant of potence2 (in a watch). Oxford English Dictionary
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Roger Richebé
Grande Maguet (1947) (director) Jean de la Lune (1949) (producer) Monseigneur (1949) (writer and producer) Gigolo (1951) (producer) Gibier de potence wikipedia.org
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potencé
potencé, a. Her. (ˈpəʊtənseɪ) Also potencie; improperly potence. [a. F. potencé, f. potence: see potence2. Cf. patonce.] = potent a.21572 J. Bossewell Armorie ii. 35 Beareth Sable, a Bende Argent, with twoo double Cotizes, Potences and Counter⁓potences of three peces d'Or. 1602 Segar Hon. Mil. & Civ... Oxford English Dictionary
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Kinwarton Dovecote
The building still houses doves to this day and is noted for its "potence" (a pivoted ladder) which provides access to the nesting boxes. wikipedia.org
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potance
potance var. potence2. Oxford English Dictionary
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Gabriel Gascon
Partial filmography Étienne Brûlé gibier de potence (1952) - Janedo Les Belles Histoires des pays d'en haut (1956–1963, TV Series) - Alexis Labranche wikipedia.org
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inport
inport, -portable, -portune, -possible, -potence obs. ff. import, etc. Oxford English Dictionary
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Amanita Pestilens
Cast Production Amanita Pestilens was the second Canadian colour film, after Étienne Brûlé gibier de potence/The Immortal Scoundrel from 1952, shot in wikipedia.org
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patonce
patonce, a. Her. (pəˈtɒns) [Of uncertain origin: app. first in Leigh, wrongly attributed to Harding (who has crosse patife); perh. a mistaken use of F. croix potencée: see potence.] In cross patonce, a cross with its arms usually expanding in a curved form from the centre, having ends somewhat like ... Oxford English Dictionary
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Dunster Dovecote
A revolving ladder, known as a "potence", was installed to allow the pigeon keeper to search the nest holes more easily. wikipedia.org
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pluripotent
pluripotent, a. Biol. (plʊərɪˈpəʊtənt) [f. pluri- + potent a.1 and n.2] = next. Hence pluriˈpotence = pluripotency.1942 J. Needham Biochem. & Morphogenesis ii. 228 The retention of pluripotence through many cleavages, followed by separation of blastomeres. Ibid. iii. 435 They are at first pluripoten... Oxford English Dictionary
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Ishvara Gita
Ishvara Gita consists of 11 chapters with over 768 verses which deals with topics such as worship of the Siva Lingam, Shiva Advaita metaphysics, Omni-Potence wikipedia.org
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$Q_p(\zeta)$ where $\zeta$ is a $p$-th root of $1$. I'm not looking for a full solution, only a hint please! Let $\zeta$ be a $p$-th root of unity in an algebraic closure of $Q_p$. Show that $Q_p(\zeta) = Q_p ((-p)^{...
For b) you can use Wilson's theorem, and the finite geometric series, i.e., $$ \epsilon=\frac{p}{(1-\zeta)^{p-1}}=\prod_{i=1}^{p-1}\frac{1-\zeta^i}{1-\zeta}=\prod_{i=1}^{p-1}\sum_{j=0}^{i-1}\zeta^j \equiv (p-1)!\equiv -1 \mod (1-\zeta) $$
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