+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?
+my $solution_counts_vec = '';
+my $all_are_over_a_million = 0;
+while (! $all_are_over_a_million)
+ $all_are_over_a_million = 1;
+ print "Y = $z_plus_d ; Ten Counts = $ten_counts\n";
+ foreach my $d (1 .. $z_plus_d-1)
+ my $z = $z_plus_d - $d;
+ my $n = $x*$x-$y*$y-$z*$z;
+ $all_are_over_a_million = 0;
+ my $c = vec($solution_counts_vec, $n, 4);
+ # Make sure it doesn't overflow.
+ vec($solution_counts_vec, $n, 4) = $c;
+ # n is monotonically increasing as a function of $d with constant