The set of automorphisms of pell forms and pell equations

Abstract

d = k(2) + 4 for some integer k >= 2. In this work, we first determined the set of automorphisms of the Pell form F-delta(x, y) = x(2) - dy(2) of discriminant delta = 4d. Later, we deduced the set of all integer solutions of the Pell equations F-delta(x, y) = +/- 1 and F-delta(x, y) = +/- k(2).