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

    for {
        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) {
    # format integer string with commas
    var neg, s = "", x -> string
    if s[1] == '-' {
        neg, s = "-", less(s, of=1)
    }
    neg ~ join(split(s, delim=-3), delim=",")
}

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"
}