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#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };
# https://stackoverflow.com/a/70414782/1030675
sub cardano_triplets {
my ($count) = @_;
for (my $u = 1; $count--; $u += 2) {
my $A = (1 + 3 * $u) / 2;
my $t = $u * $u * $u + $A * $A;
my $B = int sqrt $t;
--$B while $t % ($B * $B);
my $C = $t / ($B * $B);
say "$A $B $C";
}
}
# This finds all the triplets, but they aren't sorted so nicely.
sub cardano_triplets_all {
my ($count) = @_;
for (my $u = 1;; $u += 2) {
my $A = (1 + 3 * $u) / 2;
my $t = $u * $u * $u + $A * $A;
my $B = int sqrt $t;
while (1) {
--$B while $B && $t % ($B * $B);
last unless $B;
my $C = $t / ($B * $B);
say "$A $B $C";
return unless --$count;
--$B;
}
}
}
cardano_triplets(5);
say '-' x 10;
cardano_triplets_all(5);
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