This one is longer than a one-liner. Let's call the stringification function from the gmp library.

First, make sure you have the gmp library and the headers for it installed, eg. if you have a debian linux system, install the libgmp3-dev package. Then make a directory called Math-Tobase-1.0 and enter the following code to a file called Tobase.xs in it:

#include "EXTERN.h"
#include "perl.h"
#include "XSUB.h"

#include <gmp.h>

MODULE = Math::Tobase  PACKAGE = Math::Tobase

SV *
tobase(radix, num)
        int radix
        long num
    CODE:
        ST(0) = sv_newmortal();
        if (2 <= radix && radix <= 62 || -36 <= radix && radix <= -2) 
+{
            mpz_t big;
            mpz_init_set_si(big, num);
            if (mpz_sizeinbase(big, radix) <= 70) {
                char buf[72];
                mpz_get_str(buf, radix, big);
                sv_setpv(ST(0), buf);
            }
            mpz_clear(big);
        }
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Then enter the following to a file called lib/Math/Tobase.pm under the Math-Tobase-1.0 directory (create the subdirectories):

package Math::Tobase;

require Exporter;
require DynaLoader;
our $VERSION = "1.00";
our @ISA = (Exporter::, DynaLoader::);
our @EXPORT = "tobase";

bootstrap Math::Tobase::;

1;
__END__
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=head1 NAME

Math::Tobase - Convert integers to a string in any radix

=head1 SYNOPSIS

use Math::Tobase;
print tobase(16, 200), "\n"; # prints c8

=head1 DESCRIPTION

=over 4

=item tobase RADIX, INTEGER

Converts an integer to a string in any radix (number base), 
returning a string.  

The radix must be an integer between 2 and 62 or between -36 and -2, 
inclusive.  
If the magnitude of the radix is greater than 10 but at most 36,
lowercase letters a to z are used to indicate digits greater 
than 9; however, if the radix is greater than 36 
then digits between 10 and 35 are represented with uppercase,
and digits greater than 35 are represented with lowercase letters.

=back

=head1 INSTALLATION

This module requires the gmp (GNU MP) library, 
which you can download from L<http://gmplib.org/>.

=cut
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Then enter the following to the Makefile.PL file under the Math-Tobase-1.0 directory.

use ExtUtils::MakeMaker;

WriteMakefile(
    NAME => "Math::Tobase",
    VERSION_FROM => "lib/Math/Tobase.pm",
    LIBS => ["-lgmp"],
);
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Now compile the code with the command

perl Makefile.PL && make
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If all is successful, you can install the module now and get a Math::Tobase module with a tobase function that does what you want.

Try it out before installing using the command

perl -I./lib -Iblib/arch -we 'use Math::Tobase; print tobase(13, 54), 
+"\n";'
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The output shall be 42.

Update 2011-03-18: see also Re: Module for 128-bit integer math? for a list of bigint modules. See also Re: Convert big number from decimal to hexadecimal where I reuse this code.

Update 2012-10-16: note to self (as I reference this code frequently): you may want to use XSLoader.

Update 2013-11-19: for more XS examples, see Re: Perl XS.