Data commit

Task/Pells-equation/Perl/pells-equation.pl

@@ -0,0 +1,35 @@
+sub solve_pell {
+    my ($n) = @_;
+
+    use bigint try => 'GMP';
+
+    my $x = int(sqrt($n));
+    my $y = $x;
+    my $z = 1;
+    my $r = 2 * $x;
+
+    my ($e1, $e2) = (1, 0);
+    my ($f1, $f2) = (0, 1);
+
+    for (; ;) {
+
+        $y = $r * $z - $y;
+        $z = int(($n - $y * $y) / $z);
+        $r = int(($x + $y) / $z);
+
+        ($e1, $e2) = ($e2, $r * $e2 + $e1);
+        ($f1, $f2) = ($f2, $r * $f2 + $f1);
+
+        my $A = $e2 + $x * $f2;
+        my $B = $f2;
+
+        if ($A**2 - $n * $B**2 == 1) {
+            return ($A, $B);
+        }
+    }
+}
+
+foreach my $n (61, 109, 181, 277) {
+    my ($x, $y) = solve_pell($n);
+    printf("x^2 - %3d*y^2 = 1 for x = %-21s and y = %s\n", $n, $x, $y);
+}