# Pythagorean Triplet

Easy
12
84.5% Acceptance

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.

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 `true` as 5, 4, and 3 form a Pythagorean triplet (5² + 4² = 3²).
• 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 `true` since 5, 12, and 13 form a valid Pythagorean triplet (5² + 12² = 13²).
• 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 `false` because 2, 3, and 4 do not satisfy the Pythagorean triplet equation (2² + 3² ≠ 4²).
• 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 `true`, as these numbers form a Pythagorean triplet (7² + 24² = 25²).
• 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 `false` as these numbers do not form a Pythagorean triplet (1² + 5² ≠ 8²).
• Task: Confirm that your `isPythagoreanTriplet` method can effectively identify and reject invalid triplets.