Re: a=sqrt(sqrt(b)+sqrt(k*b+1))

Vincenzo Librandi wrote:

Let a,b,k, integer,
find the solutions:

a=sqrt(sqrt(b)+sqrt(k*b+1))


of course (a,b,k)>0

b=y^2
bk+1=x^2
x+y=a^2

k*(y^2)+1=x^2
x+y=a^2

Pell's equation:

x^2-ky^2=1
for any given k and x+y=square
are infinitely many solutions.

Regards,
Vincenzo Librandi
.