This package gives provides support for finding solutions to the generalized Pell's equation.
More specifically, give an integer
To do this, you can call pellseqn(D, N=1).
This will return a (possibly infinite) iterator whose eltype is Tuple{BigInt,BigInt}.
julia> Pkg.add("PellsEquation")
julia> using PellsEquation, .Iterators
julia> collect(take(pellseqn(2), 5))
5-element Vector{Tuple{BigInt, BigInt}}:
(1, 0)
(3, 2)
(17, 12)
(99, 70)
(577, 408)
julia> collect(take(pellseqn(2, 1), 5))
5-element Vector{Tuple{BigInt, BigInt}}:
(1, 0)
(3, 2)
(17, 12)
(99, 70)
(577, 408)
julia> collect(take(pellseqn(5, -1), 5))
5-element Vector{Tuple{BigInt, BigInt}}:
(2, 1)
(38, 17)
(682, 305)
(12238, 5473)
(219602, 98209)
julia> collect(take(pellseqn(4, 25), 5))
2-element Vector{Tuple{BigInt, BigInt}}:
(5, 0)
(13, 6)
julia> collect(take(pellseqn(4, 10), 5))
Tuple{BigInt, BigInt}[]
julia> collect(take(pellseqn(921, -12), 5))
5-element Vector{Tuple{BigInt, BigInt}}:
(123013602, 4053436)
(620494807415610916348542, 20445999054572056617484)
(3129847429634131057287425640460782483138, 103131979224431202543397867947637928044)
(15787311699815721226111492312624904230758974206686324318, 520209607285982995690281237198588485553526346187087196)
(79633022474924155281204153475574155565247711565894067613899610557324322, 2623997304693724359853375113257533978570443685138259398969894101570076)