Modèl Lhermite yo

Modèl Lhermite yo pèmèt ke nou sentetize yon pakèt eleman oubyen objè ant yo.
Modèl Lhermite yo pèmèt sentetize...

## Modèl flèch Jonatan de fason jeneral

1 S 20 v 20 konsène lansman flèch, nou kapab li chapit 20 an pou nou ka genyen yon meyè ide . 
Gen 3 posibilite lè ou lanse yon flèch.

Tout swit kwasant nonm antye kapab ekri konsa :

\mathbb{U}_n=\sum_{i=1}^{f\left(n\right)}{\left(\left[\frac{1+\sum_{m=1}^{i}{\varphi\left(m\right)}}{n+1}\right]\times\left[\frac{n+1}{1+\sum_{m=1}^{i}{\varphi\left(m\right) }}\right]\times i\times\varphi\left(i\right)\right)}

e pi jeneralman :

\mathbb{U}_n=\sum_{i=1}^{f\left(n\right)}{\left(\left[\frac{\alpha+\sum_{m=1}^{i}{\varphi\left(m\right)}}{n+\alpha}\right]\times\left[\frac{n+\alpha}{\alpha+\sum_{m=1}^{i}{\varphi\left(m\right) }}\right]\times i\times\varphi\left(i\right)\right)}

avèk f\left(n\right)\geq \mathbb{U}_n    

 e  \alpha >0  

## Nonm premye ak modèl flèch Jonatan

: 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) 

: 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) 

: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) 

: 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) 

: 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) 

## Boul wouj ak boul ble nan kad nonm premye
 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

## Modèl flèch nan kad nonm premye annakò avèk teyorèm Wilson

: \forall n \in \mathbb{N'} 

: (n-1)! \equiv\ -1 \pmod n \Leftrightarrow n \in \mathbb{P}  

Nou kapab avanse

: \forall n \in \mathbb{N'} 

: \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}  

li evidan 

:\forall n \in \mathbb{N'} 

: \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}  

Alò annakò avèk modèl Lhermite yo ak teyorèm Wilson yo, nou gen teyorèm sa yo :

: \forall n \in \mathbb{N^*} 

: \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}

: \forall n \in \mathbb{N^*} 

: \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}

Nou gen relasyon sa yo

: \forall n \in \mathbb{N^*} 

: \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] 

an chwazi you nan fòmil yo

: 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) 

an ranplase

 
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] 

an ranplase

 
1-\left[\frac{\left[ {\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}\right] pa \left[ \frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right] 

e

 
1-\left[\frac{\left[ {\frac{\left(i!\right)^2}{i^3}}\right]}{\frac{\left(i!\right)^2}{i^3}}\right] pa \left[ \frac{\left[\frac{\left(i-1\right)!+1}{i}\right]}{\frac{\left(i-1\right)!+1}{i}}\right]-\left[\frac{1}{i}\right] 

Yon ekspresyon ekivalant se :

:P_n = \sum_{i=1}^{2^{2^{n}}}{\left(\left[ \frac{1+\sum_{m=1}^i{\left(\left[\frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right]\right)}}{n+1} \right]\times \left[  \frac{n+1}{1+\sum_{m=1}^i{\left(\left[\frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right]\right)}} \right]\times i \times \left( \left[\frac{\left[\frac{\left(i-1\right)!+1}{i}\right]}{\frac{\left(i-1\right)!+1}{i}}\right]-\left[\frac{1}{i}\right]\right) \right) }

## Boul wouj ak boul ble nan kad nonm premye annakò avèk teyorèm Wilson

An nou fè menm bagay pou :

 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
## Boul wouj ak boul ble nan kad nonm premye Mèsèn

Klike sou referans lan pou ka wè youn nan fòmil yo 

## Boul wouj ak boul ble nan kad nonm premye Mèsèn annakò avèk teyorèm Wilson

## Fonksyon &Omega; annakò ak modèl Lhermite yo

: \Omega\left(n\right)=\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left(\right]\right)}\right)}}\right)
## Fonksyon Liouville ak modèl Lhermite yo

: \lambda\left(n\right)=\left(-1\right)^{\left(\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left(\right]\right)}\right)}}\right)\right)}

## Gade tou
* Postila Bètran
* Fonksyon ki konte kantite divizè n
* Fonksyon ki konte kantite nonm premye jimo yo
* Fonksyon ki konte nonm premye ki sou fòm an+b lè a ak b premye entre yo
* Fonksyon lanmbda Liouville
* Fonksyon pi
* Fonksyon Omega ki konte kantite faktè premye ki rantre nan dekonpozisyon yon nonm antye n
* Fonksyon omega ki konte kantite nonm premye ki diferan ki divize yon nonm n
* Fonksyon phi Euler
* Fonksyon pi, ki konte kantite nonm premye
* Fonksyon psi Tchebycheff
* Fonksyon tèta Tchebycheff
* Fonksyon Von Mangolt
* Fòmil pou nonm konpoze
* Modèl boul wouj ak boul ble
* Modèl flèch Jonatan
* Modèl Lhermite yo
* Modèl mouton lòt patiraj
* Modèl pitit pwodig ou modèl ti mouton pèdi
* Modèl predesesè
* Modèl siksesè
* Modèl ti triyang ak gwo triyang
* Modèl triyang ak kwadrilatè
* Nonm pafè
* Nonm premye ak modèl boul wouj ak boul ble
* Nonm premye Ezau
* Nonm premye Fermat
* Nonm premye Izaak
* Nonm premye Jakòb
* Nonm premye Mersenne
* Nonm zanmi
* Primoryel
* Pwisansyèl
* Rezolisyon ekasyon premye degre ak sentèz

## Referans

## Lyen deyò