# Pythagorean Triplet

In this lab, you will implement a method in Java named `isPythagoreanTriplet`

. This method will take an array of three numbers as input and return a boolean value indicating whether these numbers form a Pythagorean triplet.

### What is a Pythagorean Triplet?

A Pythagorean triplet consists of three positive integers (a), (b), and (c), such that (a^2 + b^2 = c^2). For example, (3, 4, 5) is a Pythagorean triplet because 3² + 4² = 5².

### Task

Your task is to create a method `isPythagoreanTriplet(int[] numbers)`

in the `Main`

class. This method should:

- Take an array of three integers as its parameter.
- Check if these integers can form a Pythagorean triplet.
- Return
`true`

if they form a Pythagorean triplet, and`false`

otherwise.

### Implementation Guidelines

**Sorting**: Consider sorting the array first. This can simplify the process of comparing the squares of the numbers.**Math Operations**: You'll need to perform squaring and sum operations to check if the numbers satisfy the Pythagorean condition.**Edge Cases**: Be sure to handle edge cases such as negative numbers or zeros, as these do not form valid triplets.

Remember, no external libraries are required; standard Java functions are sufficient to complete this task.

### Goal

Successfully implement the `isPythagoreanTriplet`

method to pass all the challenges, proving that your method can accurately identify Pythagorean triplets as well as reject non-triplets.

### Challenges

#### Challenge 1: Test Basic Pythagorean Triplet

**Input**: An array`[5, 4, 3]`

**Expected Behavior**: Your function should**return**as 5, 4, and 3 form a Pythagorean triplet (5² + 4² = 3²).`true`

**Task**: Implement the`isPythagoreanTriplet`

method in the`Main`

class to correctly identify this triplet.

#### Challenge 2: Test Larger Pythagorean Triplet

**Input**: An array`[5, 12, 13]`

**Expected Behavior**: Your function should**return**since 5, 12, and 13 form a valid Pythagorean triplet (5² + 12² = 13²).`true`

**Task**: Ensure that your`isPythagoreanTriplet`

method can handle larger integers and still accurately determine a Pythagorean triplet.

#### Challenge 3: Test with Non-Triplet

**Input**: An array`[2, 3, 4]`

**Expected Behavior**: The function should**return**because 2, 3, and 4 do not satisfy the Pythagorean triplet equation (2² + 3² ≠ 4²).`false`

**Task**: Modify`isPythagoreanTriplet`

to correctly reject arrays that do not form a Pythagorean triplet.

#### Challenge 4: Test Complex Pythagorean Triplet

**Input**: An array`[7, 25, 24]`

**Expected Behavior**: Your function should**return**, as these numbers form a Pythagorean triplet (7² + 24² = 25²).`true`

**Task**: This challenge tests the function's ability to recognize less obvious triplets. Ensure your method can identify such cases accurately.

#### Challenge 5: Test Another Non-Triplet

**Input**: An array`[1, 5, 8]`

**Expected Behavior**: The function should**return**as these numbers do not form a Pythagorean triplet (1² + 5² ≠ 8²).`false`

**Task**: Confirm that your`isPythagoreanTriplet`

method can effectively identify and reject invalid triplets.