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## to Difference Of Squares in the Lua Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

#### Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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.

## Running the tests

To run the tests, run the command `busted` from within the exercise directory.

## Further information

For more detailed information about the Lua track, including how to get help if you're having trouble, please visit the exercism.io Lua language page.

## Source

Problem 6 at Project Euler http://projecteuler.net/problem=6

## Submitting Incomplete Solutions

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

### difference-of-squares_spec.lua

``````local diff = require('difference-of-squares')

describe('difference-of-squares', function()
describe('square_of_sums', function()
it('should square the sum of the numbers up to the given number', function()
assert.equal(225, diff.square_of_sums(5))
assert.equal(3025, diff.square_of_sums(10))
assert.equal(25502500, diff.square_of_sums(100))
end)
end)

describe('sum_of_squares', function()
it('should sum the squares of the numbers up to the given number', function()
assert.equal(55, diff.sum_of_squares(5))
assert.equal(385, diff.sum_of_squares(10))
assert.equal(338350, diff.sum_of_squares(100))
end)
end)

describe('difference_of_squares', function()
it('should subtract sum of squares from square of sums', function()
assert.equal(0, diff.difference_of_squares(0))
assert.equal(170, diff.difference_of_squares(5))
assert.equal(2640, diff.difference_of_squares(10))
assert.equal(25164150, diff.difference_of_squares(100))
end)
end)
end)``````
``````local degree = 2

local function square_of_sums(n)
local sum = 0
for i = 0, n do
sum = sum + i
end
return math.pow(sum, degree)
end

local function sum_of_squares(n)
local sum = 0
for i = 0, n do
sum = sum + math.pow(i, degree)
end
return sum
end

local function difference_of_squares(n)
return square_of_sums(n) - sum_of_squares(n)
end

return {
square_of_sums = square_of_sums,
sum_of_squares = sum_of_squares,
difference_of_squares = difference_of_squares
}``````