f(n)=n^2+2n =>x^2-Ay^2=1

If n>=2 (even and integer)

Then for all n

f(n)=n^2+2n

to produce the Pell's equation.

x^2-Ay^2=1

example:
n=2, f(n)=8, then
1^2+8=3^2; 3^2-2*2^2=1

n=4, f(n)=24, then
1^2+24=5^2; 5^2-6*2^2=1

n=6, f(n)=48, then
1^2+48=7^2; 7^2-12*2^2=1

n=8, f(n)=80, then
1^2+80=9^2; 9^2-20*2^2=1

n=10, f(n)=120, then
1^2+120=11^2; 11^2-30*2^2=1

===========================
and so on

Regards,
Vincenzo Librandi
vincenzo.librandweoz@xxxxxxxx
.