Initial data commit

Task/Pells-equation/Sidef/pells-equation.sidef

@@ -0,0 +1,32 @@
+func solve_pell(n) {
+
+    var x = n.isqrt
+    var y = x
+    var z = 1
+    var r = 2*x
+
+    var (e1, e2) = (1, 0)
+    var (f1, f2) = (0, 1)
+
+    loop {
+
+        y = (r*z - y)
+        z = floor((n - y*y) / z)
+        r = floor((x + y) / z)
+
+        (e1, e2) = (e2, r*e2 + e1)
+        (f1, f2) = (f2, r*f2 + f1)
+
+        var A = (e2 + x*f2)
+        var B = f2
+
+        if (A**2 - n*B**2 == 1) {
+            return (A, B)
+        }
+    }
+}
+
+for n in [61, 109, 181, 277] {
+    var (x, y) = solve_pell(n)
+    printf("x^2 - %3d*y^2 = 1 for x = %-21s and y = %s\n", n, x, y)
+}