Lhermite's models


Lhermite's models are interesting ways to synthesize various objects that are apparently scattered.

Prime numbers and the model of three arrowsEdit

 

 

with   and  



 
 
 
 
 

Red balls and blue balls and prime numbersEdit

 

Red balls and blue balls and prime numbers according to Wilson's theoremEdit

Prime numbers and the model of three arrows according to Wilson's theoremEdit

 
 

in the same way, it is advanced that

 
 

It's very evident that

 
 

Therefore, according to Lhermite's models and Wilson's theorem, there are two evident theorems :

 
 
 
 

Therefore the following relation becomes true :

 
 


Let's choose one of the formulas that are indicated in the first section :

 


let's replace

 

and

 

Therefore an equivalent expression is :

 

Function Ω according to Lhermite's modelsEdit

 

Liouville's function and Lhermite's modelsEdit

 

Three Arrows or Jonatan's ArrowsEdit

There are three possibilities :  or   or   . In the same way , there are three possibilities :   or   or  

with

ReferencesEdit

See alsoEdit