# Module 01 Project

## Introduction

In this PA you will write a few Ruby methods to practice Ruby syntax and explore the standard Ruby classes.

Project starter files: `p1.zip`

## Requirements

`factors(n)`

— must return an Array of all the factors of n, in order and
without duplicates. The result must be [] if n < 1. For examples, ```
factors(1) ==
[1]
```

and `factors(12) == [1,2,3,4,6,12]`

.

`primes(n)`

— must return an Array of all prime numbers less than or equal to n,
in order and without duplicates. primes must return [] if n < 2. For examples,
`primes(10) == [2,3,5,7]`

.

`prime_factors(n)`

— must return an Array of all prime factors of n, in order and
without duplicates. `prime_factors`

must return [] if n < 2. For examples,
`prime_factors(1) == []`

and `prime_factors(12) == [2,3]`

.

`perfects(n)`

— must return an Array of all perfect numbers less than or equal
to n, in order and without duplicates. A perfect number is one whose factors sum
to twice the number. For example, `perfects(10) == [6]`

(because the factors of 6
are 1, 2, 3, and 6, and these sum to 12).

`pythagoreans(n)`

— must return an Array of Arrays of Pythagorean triples whose
elements are all less than or equal to n, in order without duplicates, and such
that each triple is ordered. A Pythagorean triple is three positive integers (x,
y, z) such that x^{2} + y^{2} = z^{2}. For example,
`pythagoreans(15) == [[3,4,5], [5,12,13], [6,8,10], [9,12,15]]`

.

The Integer iterator `upto()`

is quite useful in solving these problems.
Alternatively, you can use Ranges. The Array `select`

method is also useful.
You may assume that all of the `n`

parameters are instances of the `Integer`

class or one of its descendants.

Some test routines are included in `test.rb`

. However, your submission will be
graded based on additional tests not provided to you, so you should write your
own test cases as well. You may need to install the unit test package (```
gem
install test-unit
```

) if your distribution of Ruby does not come pre-loaded with
it.

For this assignment, you may NOT use any classes or methods that are not in the
Ruby Core (i.e., you shouldn’t `require`

anything). If you are unsure about a
particular class or method, you can consult the documentation. Also, we will
test your submission using Ruby 2.6 so you shouldn’t depend on any features
added after that version.

## Submission

Your program must contain implementations of the five methods described above.
You must name your Ruby script file `p1.rb`

. You must put your name in a comment
at the top of the file. As usual, decompose your methods to make them more
readable, use good names, indent properly (indentation is conventionally two
spaces in Ruby), and so on. You will partly be graded on the readability of your
code but mostly on whether it works.

Submit ONLY `p1.rb`

to the appropriate assignment on Canvas by the deadline.