pgcd.py

Created on March 27, 2025

692 Bytes

PGCD(a;b)=PGCD(a-b;b)
PGCD(ka;kb)=kPGCD(a;b)

Identité de Bézout :

Si d = PGCD(a;b) alors il existe
des entiers relatifs u et v tq 
au + bv = d

Théorème de Bézout :

a et b premiers entre eux ssi 
il existe des entiers relatifs
u et v tq au + bv = 1 

Théorème de Gauss : 
  
Si a divise le produit bc et si
a est premier avec b alors a
divise c 

Corollaire du théorème de Gauss :

Si b et c divisent a et sont 
premiers entre eux alors le
produit bc divise a

Equation dionphantienne :
  
1. Chercher un couple solution 
2. Chercher y grâce au th de 
Gauss, puis chercher x en 
remplacant y dans l'équation
3. Réciproquement, si x=...
et y=..., 
S={(...;...), k€Z}

During your visit to our site, NumWorks needs to install "cookies" or use other technologies to collect data about you in order to:

Ensure the proper functioning of the site (essential cookies); and
Track your browsing to send you personalized communications if you have created a professional account on the site and can be contacted (audience measurement cookies).

With the exception of Cookies essential to the operation of the site, NumWorks leaves you the choice: you can accept Cookies for audience measurement by clicking on the "Accept and continue" button, or refuse these Cookies by clicking on the "Continue without accepting" button or by continuing your browsing. You can update your choice at any time by clicking on the link "Manage my cookies" at the bottom of the page. For more information, please consult our cookies policy.

Accept and continue Continue without accepting

My Python Scripts

Library

My scripts

My calculator

pgcd.py