Ukryta treść:
(szkic) Można załozyc iż \(\displaystyle{ NWD(a,b)= d=1}\) (inaczej \(\displaystyle{ d |x_k}\)); a zatem
\(\displaystyle{ NWD(a, x_k)=1}\) dla k>0,
Niech k>0; z ZSD dla \(\displaystyle{ x_k+ 1}\) liczb: \(\displaystyle{ x_k, x_{k+1}, ...x_{k+x_k}}\);istnieją \(\displaystyle{ p>q}\): \(\displaystyle{ x_k | x_p-x_q}\)
oraz \(\displaystyle{ x_p-x_q=a(x_{p-1}-x_{q-1})}\) wiec
\(\displaystyle{ x_k | x_{p-1}-x_{q-1}}\) itd az \(\displaystyle{ x_k | x_{k+p-q}-x_k}\) tj. \(\displaystyle{ 1< x_k | x_{k+p-q}}\)
cbdo
\(\displaystyle{ NWD(a, x_k)=1}\) dla k>0,
Niech k>0; z ZSD dla \(\displaystyle{ x_k+ 1}\) liczb: \(\displaystyle{ x_k, x_{k+1}, ...x_{k+x_k}}\);istnieją \(\displaystyle{ p>q}\): \(\displaystyle{ x_k | x_p-x_q}\)
oraz \(\displaystyle{ x_p-x_q=a(x_{p-1}-x_{q-1})}\) wiec
\(\displaystyle{ x_k | x_{p-1}-x_{q-1}}\) itd az \(\displaystyle{ x_k | x_{k+p-q}-x_k}\) tj. \(\displaystyle{ 1< x_k | x_{k+p-q}}\)
cbdo