Data commit

Task/Pells-equation/Delphi/pells-equation.delphi

@@ -0,0 +1,70 @@
+program Pells_equation;
+
+{$APPTYPE CONSOLE}
+
+uses
+  System.SysUtils,
+  Velthuis.BigIntegers;
+
+type
+  TPellResult = record
+    x, y: BigInteger;
+  end;
+
+function SolvePell(nn: UInt64): TPellResult;
+var
+  n, x, y, z, r, e1, e2, f1,  t, u, a, b: BigInteger;
+begin
+  n := nn;
+  x := nn;
+  x := BigInteger.Sqrt(x);
+  y := BigInteger(x);
+  z := BigInteger.One;
+  r := x shl 1;
+
+  e1 := BigInteger.One;
+  e2 := BigInteger.Zero;
+  f1 := BigInteger.Zero;
+  b := BigInteger.One;
+
+  while True do
+  begin
+    y := (r * z) - y;
+    z := (n - (y * y)) div z;
+    r := (x + y) div z;
+
+    u := BigInteger(e1);
+    e1 := BigInteger(e2);
+    e2 := (r * e2) + u;
+
+    u := BigInteger(f1);
+    f1 := BigInteger(b);
+
+    b := r * b + u;
+    a := e2 + x * b;
+
+    t := (a * a) - (n * b * b);
+
+    if t = 1 then
+    begin
+      with Result do
+      begin
+        x := BigInteger(a);
+        y := BigInteger(b);
+      end;
+      Break;
+    end;
+  end;
+end;
+
+const
+  ns: TArray<UInt64> = [61, 109, 181, 277];
+  fmt = 'x^2 - %3d*y^2 = 1 for x = %-21s and y = %s';
+
+begin
+  for var n in ns do
+    with SolvePell(n) do
+      writeln(format(fmt, [n, x.ToString, y.ToString]));
+
+  {$IFNDEF UNIX} readln; {$ENDIF}
+end.