Perfect Number Validator

This project implements an algorithmic check in C to determine if a user-inputted integer classifies as a Perfect Number according to number theory principles.

🧮 Mathematical Definition

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

Formally, a number $n$ is perfect if: $$\sigma_{1}(n) - n = n$$ Where $\sigma_{1}(n)$ is the sum of all positive divisors of $n$.

Example Case

For the integer 6:

• Divisors: 1, 2, 3
• Sum: $1 + 2 + 3 = 6$
• Result: ✅ Perfect Number

⚙️ Technical Implementation

• Language: C (Standard Library)
• Logic: Linear Iteration ($O(n)$ complexity).
• Process:
  1. Accepts integer input.
  2. Iterates from $1$ to $n-1$.
  3. Accumulates factors where $n \pmod i \equiv 0$.
  4. Compares the accumulator to the original input.

🚀 How to Run

1. Compile the code:

   gcc main.c -o validator

2. Run the executable:

   ./validator

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This repository demonstrates algorithmic implementation of mathematical properties using C.