+Given the positive integers, x, y, and z, are consecutive terms of an
+arithmetic progression, the least value of the positive integer, n, for which
+the equation, x2 − y2 − z2 = n, has exactly two solutions is n = 27:
+342 − 272 − 202 = 122 − 92 − 62 = 27
+It turns out that n = 1155 is the least value which has exactly ten solutions.
+How many values of n less than one million have exactly ten distinct solutions?
+(z+2d)^2 - (z+d)^2 - z^2 = z^2+4dz+4d^2 - z^2 - 2dz - d^2 - z^2 =
+-z^2 + 2dz +3d^2 = (-z + 3d)(z + d)
+my $solution_counts_vec = '';
+ print "Z = $z ; Ten Counts = $ten_counts\n" if ($z % 10_000 == 0);
+ my $n = (3*$d-$z)*($z+$d);
+ my $c = vec($solution_counts_vec, $n, 4);
+ # Make sure it doesn't overflow.
+ vec($solution_counts_vec, $n, 4) = $c;
+print "Ten counts = $ten_counts\n";