Fòmil pou nonm konpoze

Nonm konpoze yo lye ak nosyon nonm premye .

Definisyon

Yon antye natirèl n se yon konpoze si e sèlman si li pi gran ke 1 e ke li pa yon nonm premye.

Ekspresyon fonksyon karakteristik konpoze

An nou note $\mathbb {X} _{n}$ nonm konpoze rang n e $\left(\mathbb {X} _{n}\right)$ swit kwasant nonm konpoze yo.

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

1-\left[{\frac {\left[{\frac {\left(n-1\right)!+1}{n}}\right]}{\frac {\left(n-1\right)!+1}{n}}}\right]=1\Longleftrightarrow n\in \mathbb {X}

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

fonksyon karakteristik si nou dezye pa $\varphi$ nou genyen :

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

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

Ekspresyon nonm konpoze elabore pa Jean Lhermite Lainé Junior selon modèl flèch Jonathan

$\mathbb {X} _{n}=\sum _{i=1}^{4m}{\left(\left[{\frac {1+\sum _{m=1}^{i}{\varphi \left(m\right)}}{n+1}}\right]\times \left[{\frac {n+1}{1+\sum _{m=1}^{i}{\varphi \left(m\right)}}}\right]\times i\times \varphi \left(i\right)\right)}$

$\mathbb {X} _{n}=\sum _{i=1}^{2m+2}{\left(\left[{\frac {1+\sum _{m=1}^{i}{\varphi \left(m\right)}}{n+1}}\right]\times \left[{\frac {n+1}{1+\sum _{m=1}^{i}{\varphi \left(m\right)}}}\right]\times i\times \varphi \left(i\right)\right)}$

Ekspresyon nonm konpoze elabore pa Jean Lhermite Lainé Junior selon modèl boul wouj ak boul ble

Lòt Ekspresyon nonm konpoze elabore pa Jean Lhermite Lainé Junior

Gade tou

Referans

Lyen deyò