lucas-carmichael_conjecture_cached.pl

#!/usr/bin/perl

# Lucas-Carmichael numbers: squarefree composite numbers n such that p | n => p+1 | n+1.

# It is not known whether any Lucas–Carmichael number is also a Carmichael number.

# See also:
#   https://oeis.org/A006972
#   https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael_number

use 5.020;
use strict;
use warnings;
use experimental qw(signatures);

use Storable;
use Math::GMPz;
use ntheory qw(:all);
use Math::Prime::Util::GMP;
use experimental qw(signatures);

my $carmichael_file       = "cache/factors-carmichael.storable";
my $lucas_carmichael_file = "cache/factors-lucas-carmichael.storable";

my $carmichael       = retrieve($carmichael_file);
my $lucas_carmichael = retrieve($lucas_carmichael_file);

foreach my $key (keys %$lucas_carmichael) {
    if (exists $carmichael->{$key}) {
        die "Found counter-example: $key";
    }
}

say "No counter-example found...";