Lhermite's models


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

Prime numbers and the model of three arrows

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with   and  



 
 
 
 
 

Red balls and blue balls and prime numbers

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

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

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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 models

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Liouville's function and Lhermite's models

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Three Arrows or Jonatan's Arrows

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

with

References

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See also

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