Data commit

Task/Pells-equation/Nim/pells-equation.nim

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+import math, strformat
+import bignum
+
+func solvePell(n: int): (Int, Int) =
+  let x = newInt(sqrt(n.toFloat).int)
+  var (y, z, r) = (x, newInt(1), x shl 1)
+  var (e1, e2) = (newInt(1), newInt(0))
+  var (f1, f2) = (newInt(0), newInt(1))
+
+  while true:
+    y = r * z - y
+    z = (n - y * y) div z
+    r = (x + y) div z
+
+    (e1, e2) = (e2, e1 + e2 * r)
+    (f1, f2) = (f2, f1 + f2 * r)
+
+    let (a, b) = (f2 * x + e2, f2)
+    if a * a - n * b * b == 1:
+      return (a, b)
+
+for n in [61, 109, 181, 277]:
+  let (x, y) = solvePell(n)
+  echo &"x² - {n:3} * y² = 1 for (x, y) = ({x:>21}, {y:>19})"