Data commit

Task/Pells-equation/Go/pells-equation.go

@@ -0,0 +1,62 @@
+package main
+
+import (
+    "fmt"
+    "math/big"
+)
+
+var big1 = new(big.Int).SetUint64(1)
+
+func solvePell(nn uint64) (*big.Int, *big.Int) {
+    n := new(big.Int).SetUint64(nn)
+    x := new(big.Int).Set(n)
+    x.Sqrt(x)
+    y := new(big.Int).Set(x)
+    z := new(big.Int).SetUint64(1)
+    r := new(big.Int).Lsh(x, 1)
+
+    e1 := new(big.Int).SetUint64(1)
+    e2 := new(big.Int)
+    f1 := new(big.Int)
+    f2 := new(big.Int).SetUint64(1)
+
+    t := new(big.Int)
+    u := new(big.Int)
+    a := new(big.Int)
+    b := new(big.Int)
+    for {
+        t.Mul(r, z)
+        y.Sub(t, y)
+        t.Mul(y, y)
+        t.Sub(n, t)
+        z.Quo(t, z)
+        t.Add(x, y)
+        r.Quo(t, z)
+        u.Set(e1)
+        e1.Set(e2)
+        t.Mul(r, e2)
+        e2.Add(t, u)
+        u.Set(f1)
+        f1.Set(f2)
+        t.Mul(r, f2)
+        f2.Add(t, u)
+        t.Mul(x, f2)
+        a.Add(e2, t)
+        b.Set(f2)
+        t.Mul(a, a)
+        u.Mul(n, b)
+        u.Mul(u, b)
+        t.Sub(t, u)
+        if t.Cmp(big1) == 0 {
+            return a, b
+        }
+    }
+}
+
+func main() {
+    ns := []uint64{61, 109, 181, 277}
+    for _, n := range ns {
+        x, y := solvePell(n)
+        fmt.Printf("x^2 - %3d*y^2 = 1 for x = %-21s and y = %s\n", n, x, y)
+    }
+}