The following script employs Zeckendorf's_theorem and prints the Zeckendorf representation for a given number.

#!/usr/bin/perl

use strict;
use warnings;

zeck($ARGV[0]);

sub zeck {
    if (is_fibonnacci($_[0])) {
        print "$_[0]\n";
        exit;
    }
    my $count = 0;
    my $prev = 0;
    my $curr = 0;
    while (($curr = fibonnacci($count)) < $_[0]) {
        $prev = $curr;
        $count++;
    }
    print "$prev\n";
    zeck($_[0] - $prev);
}

sub fibonnacci {
    my $a = 0;
    my $b = 1;
    for (0..$_[0]) {
        my $c = $a;
        $a = $b;
        $b = $c + $b;
    }
    return $a;
}

sub is_fibonnacci {
    my $plus = (5 * $_[0] * $_[0]) + 4;
    my $mins = (5 * $_[0] * $_[0]) - 4;
    return is_perfect_square($plus) || is_perfect_square($mins);
}

sub is_perfect_square {
    my $sqrt = int(sqrt($_[0]));
    return $sqrt * $sqrt == $_[0];
}

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In reply to Zeckendorf representation by thmsdrew

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