C++ Program to Check Pronic Number

Posted in C++ Tutorial

Updated on Jan 11, 2024

By Mari Selvan

👁️ 48 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, mathematical patterns and properties often become interesting challenges. One such intriguing concept is the "Pronic Number."

A pronic number, also known as a rectangular number, oblong number, or heteromecic number, is the product of two consecutive integers.

In this tutorial, we will delve into a C++ program designed to check whether a given number is a pronic number or not.

📄 Example

Now, let's explore the C++ code that checks whether a given number is a pronic number or not.

isPronic.cpp

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#include <iostream>
#include <cmath>

// Function to check if a number is a pronic number
bool isPronic(int num) {
  int sqrtNum = std::sqrt(num);

  return (sqrtNum * (sqrtNum + 1) == num);
}

// Driver program
int main() {
  // Replace this value with your desired number
  int number = 12;

  // Check if the number is a pronic number
  if (isPronic(number)) {
    std::cout << number << " is a pronic number." << std::endl;
  } else {
    std::cout << number << " is not a pronic number." << std::endl;
  }

  return 0;
}

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the main function.

Output

12 is a pronic number.

Compile and run the program to check if the given number is a pronic number.

🧠 How the Program Works

The program defines a function isPronic that takes a number as input and returns true if the number is a pronic number and false otherwise.
Inside the function, it calculates the square root of the input number.
It checks whether the product of the square root and the square root incremented by 1 equals the input number. If yes, the number is a pronic number.
The driver program tests the function with a sample number and prints the result.

📏 Between the Given Range

Let's take a look at the C++ code that checks for pronic numbers in the range from 1 to 20.

isPronic.c

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#include <iostream>

// Function to check if a number is Pronic
bool isPronic(int num) {
  for (int i = 0; i <= num; ++i) {
    if (i * (i + 1) == num) {
      return true;
    }
  }
  return false;
}

// Function to display Pronic numbers in the range 1 to 20
void displayPronicNumbers() {
  std::cout << "Pronic Numbers in the range 1 to 20:\n";

  for (int i = 1; i <= 20; ++i) {
    if (isPronic(i)) {
      std::cout << i << " ";
    }
  }

  std::cout << "\n";
}

// Driver program
int main() {
  // Call the function to display Pronic numbers
  displayPronicNumbers();

  return 0;
}

💻 Testing the Program

Output

Pronic Numbers in the range 1 to 20:
2 6 12 20

Simply compile and run the program to see the Pronic numbers in the specified range.

🧠 How the Program Works

The program defines a function isPronic that checks if a given number is a Pronic number.
The function uses a loop to iterate through numbers from 0 to the given number and checks if i × ( i + 1 ) equals the input number.
The displayPronicNumbers function iterates through the range from 1 to 20 and calls isPronic to check if each number is Pronic.
Pronic numbers are displayed as output.

🧐 Understanding the Concept of Pronic Numbers

Before delving into the code, let's take a moment to understand the concept of pronic numbers.

A pronic number is a product of two consecutive integers, and it has applications in various mathematical and geometric contexts.

A pronic number, denoted by P_n, is a number of the form P_n=n × (n+1) where n is a non-negative integer. The sequence of pronic numbers starts as 0, 2, 6, 12, 20, and so on.

For example, let's take n = 3. The corresponding pronic number would be P₃ = 3x(3+1) = 12.