RECHERCHE DES COEFFICIENTS DE BÉZOUT

#include <iostream>

void Bezout(int rkm2,int rkm1,int ukm1=0,int vkm1=1,int ukm2=1,int vkm2=0){
/*r(k-4)=r(k-3)*q(k-2)+r(k-2) <=> r(k-2)=a*u(k-2)+b*v(k-2)
 *r(k-3)=r(k-2)*q(k-1)+r(k-1) <=> r(k-1)=a*u(k-1)+b*v(k-1)
 *r(k-2)=r(k-1)*q(k)+r(k)     <=> r(k)=a*u(k)+b*v(k) avec u(k)=u(k-2)-qk*u(k-1) et v(k)=v(k-2)-qk*v(k-1)*/
    int rk=rkm2%rkm1;
    int qk=(rkm2-rk)/rkm1;
    if(rk==0) 
        std::cout<<rkm1<<"=a*"<<ukm1<<"+b*"<<vkm1<<std::endl;
    else 
        Bezout(rkm1,rk,ukm2-qk*ukm1,vkm2-qk*vkm1,ukm1,vkm1);
    return;
}

int main(int argc,char* argv[]){
    int a,b;
    std::cout<<"a=";std::cin>>a;
    std::cout<<"b=";std::cin>>b;
    if(a<=0 || b<=0)
        std::cout<<"On suppose a et b strictement positifs."<<std::endl;
    else
        Bezout(a,b);
    return 0;
}