TASK #1 - Fibonacci Words

You are given two strings having same number of digits, $a and $b.

Write a script to generate Fibonacci Words by concatenation of the
previous two strings. Finally print 51st digit of the first term having
at least 51 digits.

Example:

    Input: $a = '1234' $b = '5678'
    Output: 7

    Fibonacci Words:

    '1234'
    '5678'
    '12345678'
    '567812345678'
    '12345678567812345678'
    '56781234567812345678567812345678'
    '1234567856781234567856781234567812345678567812345678'

    The 51st digit in the first term having at least 51 digits
    '1234567856781234567856781234567812345678567812345678' is 7.

MY NOTES: Pretty easy.  Fibonacci words == append two previous strings.
Use -d (debug mode) to see all the above explanatory info.


TASK #2 - Square-free Integer

Write a script to generate all square-free integers <= 500.

In mathematics, a square-free integer (or squarefree integer) is an
integer which is divisible by no perfect square other than 1. That is,
its prime factorization has exactly one factor for each prime that
appears in it. For example, 10 = 2 * 5 is square-free, but 18 = 2 *
3 * 3 is not, because 18 is divisible by 9 = 3**2.

Example

The smallest positive square-free integers are
    1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...

MY NOTES: also pretty easy.  The second definition above suggests using prime
numbers, which is easy enough, especially as I have a prime generating module,
but actually it's simpler to do it without primes as the first definition hints.