Lhermite's models

From Wikiversity
Jump to navigation Jump to search


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

Prime numbers and the model of three arrows[edit]

with and



Red balls and blue balls and prime numbers[edit]

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

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

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[edit]

Liouville's function and Lhermite's models[edit]

Three Arrows or Jonatan's Arrows[edit]

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

with

References[edit]

See also[edit]