Square Difference of Two large Consecutive Numbers

Given two positive consecutive numbers M and N, the task is to find the square difference of the two numbers without computing the square of those numbers.

Examples:

Input: N = 4, M = 5
Output: 9
Explanation:
52 – 42 = 25 – 16 = 9.

Input: N = 999999999, M = 1000000000
Output: 1999999999

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to use the algebraic expression to solve this problem. It is given in the question that M = N + 1. Therefore:

• The value to be computed is M2 – N2.
• On replacing M with N + 1, the above equation becomes:
```(N + 1)2 - N2
```
• (N + 1)2 can be expanded to:
`N2 + 12 + 2 * N - N2`
• On simplifying, the above equation becomes:
```1 + 2 * N
1 + N + N
(1 + N) + N
M + N
```
• Therefore, we simply need to compute and return the value of M + N.

Below is the implementation of the above approach:

CPP

 `// C++ program to find the square ` `// difference of two large ` `// consecutive numbers ` ` `  `#include ` `using` `namespace` `std; ` `typedef` `long` `long` `l; ` ` `  `// Function to find the square ` `// difference of two large ` `// consecutive numbers ` `l difference(l M, l N) ` `{ ` `    ``return` `M + N; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``l M = 999999999; ` `    ``l N = 1000000000; ` ` `  `    ``cout << difference(M, N) << endl; ` `} `

Java

 `// Java program to find the square ` `// difference of two large ` `// consecutive numbers ` ` `  ` `  `class` `GFG{ ` `  `  `// Function to find the square ` `// difference of two large ` `// consecutive numbers ` `static` `long` `difference(``long` `M, ``long` `N) ` `{ ` `    ``return` `M + N; ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``long` `M = ``999999999``; ` `    ``long` `N = ``1000000000``; ` `  `  `    ``System.out.print(difference(M, N) +``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Python3

 `# Python3 program to find the square ` `# difference of two large ` `# consecutive numbers ` ` `  `# Function to find the square ` `# difference of two large ` `# consecutive numbers ` `def` `difference(M, N): ` `    ``return` `M ``+` `N ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``M ``=` `999999999` `    ``N ``=` `1000000000` ` `  `    ``print``(difference(M, N)) ` ` `  `# This code is contributed by mohit kumar 29     `

C#

 `// C# program to find the square ` `// difference of two large ` `// consecutive numbers ` `using` `System; ` ` `  `public` `class` `GFG{ ` `   `  `// Function to find the square ` `// difference of two large ` `// consecutive numbers ` `static` `long` `difference(``long` `M, ``long` `N) ` `{ ` `    ``return` `M + N; ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``long` `M = 999999999; ` `    ``long` `N = 1000000000; ` `   `  `    ``Console.Write(difference(M, N) +``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```1999999999
```

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