Vèsyon jou 28 mas 2013 à 03:56 modifye L2j2 (diskisyon \| kontribisyon) 354 modifications Paj nouvo: Modèl Lhermite yo pèmèt ke nou sentetize yon pakèt eleman oubyen opjè antre yo . ==List modèl yo ==		Vèsyon jou 31 mas 2013 à 02:05 modifye defè L2j2 (diskisyon \| kontribisyon) 354 modifications →‎List modèl yo Modifikasyon swivan →
Liy 1 : Modèl Lhermite yo pèmèt ke nou sentetize yon pakèt eleman oubyen opjè antre yo . Modèl Lhermite yo pèmèt sentetize... ~~==List modèl yo ==~~ ==Nonm premye ak modèl flèch Jonatan== : <math>P_n = \sum_{i=1}^{2^{2^{n}}}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right) </math> : <math>P_n = \sum_{i=1}^{2^n}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right) </math> :<math>P_n = \sum_{i=1}^{1+n!}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right) </math> : <math>P_n = \sum_{i=1}^{2^n}\left(\left[\frac {1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}{n+1}\right]\times{\left[\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}\right]}\times{i}\times{\left({1-\left[{\frac{\left[(\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}}\right]}\right)}\right) </math> : <math>P_n = \sum_{i=1}^{2^{2^{n}} }\left(\left[\frac {1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}{n+1}\right]\times{\left[\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}\right]}\times{i}\times{\left({1-\left[{\frac{\left[(\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}}\right]}\right)}\right) </math> ==Boul rouj ak boul ble nan kad nonm premye== <math> P_{\left(\left(1-\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]\right)\times\left(\sum_{m=1}^{n}{\left(1-\left[\frac{\left[\frac{\left(m!\right)^2}{m^3}\right]}{\frac{\left(m!\right)^2}{m^3}}\right]\right)}-i\right)+i\right)}=\left(P_i-n\right)\times\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]+n</math> ==Boul rouj ak boul ble nan kad nonm premye annako avek teyorem Wilson== ==Model flèch nan kad nonm premye annako avek teyorem Wilson== : <math>\forall n \in \mathbb{N'} </math> : <math>(n-1)! \equiv\ -1 \pmod n \Leftrightarrow n \in \mathbb{P}</math> Nou kapap avanse : <math>\forall n \in \mathbb{N'} </math> : <math>\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]=1 \Leftrightarrow n \in \mathbb{P}</math> li evidan :<math>\forall n \in \mathbb{N'} </math> : <math>\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]=0 \Leftrightarrow n \notin \mathbb{P}</math> Alo annako avek modèl Lhermite yo ak teyorèm Wilson yo, nou gen teyorem sa yo : : <math>\forall n \in \mathbb{N^} </math> : <math>\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]=1 \Leftrightarrow n \in \mathbb{P}</math> : <math>\forall n \in \mathbb{N^} </math> : <math>\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]=0 \Leftrightarrow n \notin \mathbb{P}</math> Nou relasyon sa yo : <math>\forall n \in \mathbb{N^} </math> : <math>\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]= 1-\left[\frac{\left[ {\frac{\left(n!\right)^2}{n^3}}\right]}{\frac{\left(n!\right)^2}{n^3}}\right] </math> an chwazi you nan fomil yo <math>P_n = \sum_{i=1}^{2^{2^{n}}}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right) </math> an <math> 1-\left[\frac{\left[ {\frac{\left(n!\right)^2}{n^3}}\right]}{\frac{\left(n!\right)^2}{n^3}}\right] pa \left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right] </math> == Fonksyon Ω annako ak model Lhermite yo== : <math>\Omega\left(n\right)=\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left({{\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]}\times\left(1-\left[\frac{\left[\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}\right]\right)}\right)}}\right)</math> ==Fonksyon Liouville ak model Lhermite yo== : <math>\lambda\left(n\right)=\left(-1\right)^{\left(\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left({{\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]}\times\left(1-\left[\frac{\left[\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}\right]\right)}\right)}}\right)\right)}</math> ==Referans== == Wè tou== [[Bertrand's postulate]] * [[Boole]] * [[Boolean algebra]] * [[Euclid's theorem]] <!-- interwiki links --> [[es:Modelos de Lhermite]] [[fr:les modèles de Lhermite]][[en:Lhermite's Models]] [[it:i modeli di Lhermite]]

Modèl Lhermite yo: Diferans ant vèsyon yo