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 :

${𝕌}_n=\sum _{i=1}^{f\left(n\right)}(\left[\frac{1+\sum _{m=1}^i\phi \left(m\right)}{n+1}\right]\times \left[\frac{n+1}{1+\sum _{m=1}^i\phi \left(m\right)}\right]\times i\times \phi \left(i\right))$

e pi jeneralman :

${𝕌}_n=\sum _{i=1}^{f\left(n\right)}(\left[\frac{\alpha +\sum _{m=1}^i\phi \left(m\right)}{n+\alpha }\right]\times \left[\frac{n+\alpha }{\alpha +\sum _{m=1}^i\phi \left(m\right)}\right]\times i\times \phi \left(i\right))$

avèk $f\left(n\right)\ge {𝕌}_n$

e $\alpha >0$

Nonm premye ak modèl flèch Jonatan

$P_n=\sum _{i=1}^{2^{2^n}}(\lfloor \frac{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}{n+1}\rfloor \times \lfloor \frac{n+1}{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}\rfloor \times i\times \left(1-\lfloor \frac{\lfloor (\frac{{(i!)}^2}{i^3}\rfloor }{\frac{{(i!)}^2}{i^3}}\rfloor \right))$

$P_n=\sum _{i=1}^{2^n}(\lfloor \frac{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}{n+1}\rfloor \times \lfloor \frac{n+1}{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}\rfloor \times i\times \left(1-\lfloor \frac{\lfloor (\frac{{(i!)}^2}{i^3}\rfloor }{\frac{{(i!)}^2}{i^3}}\rfloor \right))$

$P_n=\sum _{i=1}^{1+n!}(\lfloor \frac{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}{n+1}\rfloor \times \lfloor \frac{n+1}{1+\sum _{m=1}^i(1-\lfloor \frac{\lfloor \frac{{(m!)}^2}{m^3}\rfloor }{\frac{{(m!)}^2}{m^3}}\rfloor )}\rfloor \times i\times \left(1-\lfloor \frac{\lfloor (\frac{{(i!)}^2}{i^3}\rfloor }{\frac{{(i!)}^2}{i^3}}\rfloor \right))$

$P_n=\sum _{i=1}^{2^n}(\left[\frac{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}{n+1}\right]\times \left[\frac{n+1}{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}\right]\times i\times \left(1-\left[\frac{[(\frac{{(i!)}^2}{i^3}]}{\frac{{(i!)}^2}{i^3}}\right]\right))$

$P_n=\sum _{i=1}^{2^{2^n}}(\left[\frac{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}{n+1}\right]\times \left[\frac{n+1}{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}\right]\times i\times \left(1-\left[\frac{[(\frac{{(i!)}^2}{i^3}]}{\frac{{(i!)}^2}{i^3}}\right]\right))$

Boul wouj ak boul ble nan kad nonm premye

$P_{((1-\left[\frac{\left[\frac{{(n!)}^2}{n^3}\right]}{\frac{{(n!)}^2}{n^3}}\right])\times (\sum _{m=1}^n(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])-i)+i)}=(P_i-n)\times \left[\frac{\left[\frac{{(n!)}^2}{n^3}\right]}{\frac{{(n!)}^2}{n^3}}\right]+n$

Modèl flèch nan kad nonm premye annakò avèk teyorèm Wilson

$\mathrm{\forall }n\in {\mathbb{N}}^{\prime }$

$(n-1)!\equiv -1(\mathrm{mod}n)\iff n\in \mathbb{P}$

Nou kapab avanse

$\mathrm{\forall }n\in {\mathbb{N}}^{\prime }$

$\left[\frac{\left[\frac{(n-1)!+1}{n}\right]}{\frac{(n-1)!+1}{n}}\right]=1\iff n\in \mathbb{P}$

li evidan

$\mathrm{\forall }n\in {\mathbb{N}}^{\prime }$

$\left[\frac{\left[\frac{(n-1)!+1}{n}\right]}{\frac{(n-1)!+1}{n}}\right]=0\iff n\notin \mathbb{P}$

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

$\mathrm{\forall }n\in {\mathbb{N}}^{\mathbb{*}}$

$\left[\frac{\left[\frac{(n-1)!+1}{n}\right]}{\frac{(n-1)!+1}{n}}\right]-\left[\frac{1}{n}\right]=1\iff n\in \mathbb{P}$

$\mathrm{\forall }n\in {\mathbb{N}}^{\mathbb{*}}$

$\left[\frac{\left[\frac{(n-1)!+1}{n}\right]}{\frac{(n-1)!+1}{n}}\right]-\left[\frac{1}{n}\right]=0\iff n\notin \mathbb{P}$

Nou gen relasyon sa yo

$\mathrm{\forall }n\in {\mathbb{N}}^{\mathbb{*}}$

$\left[\frac{\left[\frac{(n-1)!+1}{n}\right]}{\frac{(n-1)!+1}{n}}\right]-\left[\frac{1}{n}\right]=1-\left[\frac{\left[\frac{{(n!)}^2}{n^3}\right]}{\frac{{(n!)}^2}{n^3}}\right]$

an chwazi you nan fòmil yo

$P_n=\sum _{i=1}^{2^{2^n}}(\left[\frac{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}{n+1}\right]\times \left[\frac{n+1}{1+\sum _{m=1}^i(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])}\right]\times i\times \left(1-\left[\frac{[(\frac{{(i!)}^2}{i^3}]}{\frac{{(i!)}^2}{i^3}}\right]\right))$

an ranplase

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

an ranplase

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

e

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

Yon ekspresyon ekivalant se :

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

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

An nou fè menm bagay pou :

$P_{((1-\left[\frac{\left[\frac{{(n!)}^2}{n^3}\right]}{\frac{{(n!)}^2}{n^3}}\right])\times (\sum _{m=1}^n(1-\left[\frac{\left[\frac{{(m!)}^2}{m^3}\right]}{\frac{{(m!)}^2}{m^3}}\right])-i)+i)}=(P_i-n)\times \left[\frac{\left[\frac{{(n!)}^2}{n^3}\right]}{\frac{{(n!)}^2}{n^3}}\right]+n$

Boul wouj ak boul ble nan kad nonm premye Mèsèn

Klike sou referans lan pou ka wè youn nan fòmil yo

Fonksyon Ω annakò ak modèl Lhermite yo

$\mathrm{\Omega }\left(n\right)=\sum _{j=1}^n\left(\sum _{i=1}^n\left(\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]\times (1-\left[\frac{\left[\frac{{(i!)}^2}{i^3}\right]}{\frac{{(i!)}^2}{i^3}}\right])\right)\right)$

Fonksyon Liouville ak modèl Lhermite yo

$\lambda \left(n\right)={(-1)}^{\left(\sum _{j=1}^n\left(\sum _{i=1}^n\left(\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]\times (1-\left[\frac{\left[\frac{{(i!)}^2}{i^3}\right]}{\frac{{(i!)}^2}{i^3}}\right])\right)\right)\right)}$

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