Pell's equation: Difference between revisions

<syntaxhighlight lang="langur">val .fun = fn .a, .b, .c: [.b, .b * .c + .a]

val .solvePell = fn(.n) {

val .x = trunc .(n ^/ 2)

var .y, .z, .r = .x, 1, .x * 2

var .e1, .e2, .f1, .f2 = 1, 0, 0, 1

.y = .r * .z - .y

.z = (.n - .y * .y) \ .z

.r = (.x + .y) \ .z

.e1, .e2 = .fun(.e1, .e2, .r)

.f1, .f2 = .fun(.f1, .f2, .r)

val .b, .a = .fun(.e2, .f2, .x)

if .a^2 - .n * .b^2 == 1: return [.a, .b]

val .C = fn(.x) {

var .neg, .s = "", string .x -> string

if .s[1] == '-' {

.neg, .s = "-", rest .s -> rest

.neg ~ join (",", split (-3, .s))

for .n in [61, 109, 181, 277, 8941] {

val .x, .y = .solvePell(.n)

writeln "x² - {{.n}}y² = 1 for:\n\tx = {{.x:fn C}}\n\ty = {{.y:fn C}}\n"