# Difference Of Squares

Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.

The square of the sum of the first ten natural numbers is
(1 + 2 + ... + 10)² = 55² = 3025.

The sum of the squares of the first ten natural numbers is
1² + 2² + ... + 10² = 385.

Hence the difference between the square of the sum of the first
ten natural numbers and the sum of the squares of the first ten
natural numbers is 3025 - 385 = 2640.

You are not expected to discover an efficient solution to this yourself from
first principles; research is allowed, indeed, encouraged. Finding the best
algorithm for the problem is a key skill in software engineering.


Run the tests with:

```bash
bats difference_of_squares_test.sh
```

After the first test(s) pass, continue by commenting out or removing the
`[[ $BATS_RUN_SKIPPED == true ]] || skip` 
annotations prepending other tests.

To run all tests, including the ones with `skip` annotations, run:

```bash
BATS_RUN_SKIPPED=true bats difference_of_squares_test.sh
```

## Source

Problem 6 at Project Euler [http://projecteuler.net/problem=6](http://projecteuler.net/problem=6)


## External utilities
`Bash` is a language to write "scripts" -- programs that can call
external tools, such as
[`sed`](https://www.gnu.org/software/sed/),
[`awk`](https://www.gnu.org/software/gawk/),
[`date`](https://www.gnu.org/software/coreutils/manual/html_node/date-invocation.html)
and even programs written in other programming languages, 
like [`Python`](https://www.python.org/).
This track does not restrict the usage of these utilities, and as long
as your solution is portable between systems and does not require
installation of third party applications, feel free to use them to solve
the exercise.

For an extra challenge, if you would like to have a better understanding
of the language, try to re-implement the solution in pure `Bash`,
without using any external tools. Note that there are some types of
problems that bash cannot solve, such as performing floating point
arithmetic and manipulating dates: for those, you must call out to an
external tool.

## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others
have completed the exercise.