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# Loeschian Number

• Last Updated : 05 Apr, 2021

Given a number N, the task is to check if N is an Loeschian Number or not. If N is an Loeschian Number then print “Yes” else print “No”.

A number N is a Loeschian Number if N can be expressed of the form for any two integers x and y.

Examples:

Input: N = 19
Output:Yes
Explanation:
19 = 22+ 2*3 +32
Input: N = 20
Output: No

Approach: The idea is to iterate two nested loops in the range [0, sqrt(N)] for x and y respectively. If for any pairs of integers (x, y) satisfy the equation then print “Yes” else print “No”.
Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to check if N is a``// Loeschian Number``bool` `isLoeschian(``int` `n)``{``    ``// Iterate [0, sqrt(N)] for x``    ``for` `(``int` `x = 1; x <= ``sqrt``(n); x++) {` `        ``// Iterate [0, sqrt(N)] for y``        ``for` `(``int` `y = 1; y <= ``sqrt``(n); y++) {` `            ``// Check the given criteria``            ``if` `(x * x + x * y + y * y == n)``                ``return` `true``;``        ``}``    ``}` `    ``// If no such pair found then``    ``// return false``    ``return` `false``;``}` `// Driver Code``int` `main()``{``    ``// Given Number N``    ``int` `N = 19;` `    ``// Function Call``    ``if` `(isLoeschian(n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;``}`

## Java

 `// Java program for the above approach``class` `GFG{` `// Function to check if N is a``// Loeschian Number``static` `boolean` `isLoeschian(``int` `n)``{``    ` `    ``// Iterate [0, sqrt(N)] for x``    ``for``(``int` `x = ``1``; x <= Math.sqrt(n); x++)``    ``{``        ` `       ``// Iterate [0, sqrt(N)] for y``       ``for``(``int` `y = ``1``; y <= Math.sqrt(n); y++)``       ``{``           ` `          ``// Check the given criteria``          ``if` `(x * x + x * y + y * y == n)``              ``return` `true``;``       ``}``    ``}` `    ``// If no such pair found then``    ``// return false``    ``return` `false``;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Given Number N``    ``int` `n = ``19``;` `    ``// Function Call``    ``if` `(isLoeschian(n))``    ``{``        ``System.out.println(``"Yes"``);``    ``}``    ``else``    ``{``        ``System.out.println(``"No"``);``    ``}``}``}` `// This code is contributed by Pratima Pandey`

## Python3

 `# Python3 program for the above approach``import` `math` `# Function to check if N is a``# Loeschian Number``def` `isLoeschian(n):` `    ``# Iterate [0, sqrt(N)] for x``    ``for` `x ``in` `range``(``1``, (``int``)(math.sqrt(n)) ``+` `1``):` `        ``# Iterate [0, sqrt(N)] for y``        ``for` `y ``in` `range``(``1``, (``int``)(math.sqrt(n)) ``+` `1``):` `            ``# Check the given criteria``            ``if` `(x ``*` `x ``+` `x ``*` `y ``+` `y ``*` `y ``=``=` `n):``                ``return` `True` `    ``# If no such pair found then``    ``# return false``    ``return` `False` `# Driver code` `# Given Number N``N ``=` `19` `# Function Call``if` `(isLoeschian(N)):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed by Vishal Maurya`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to check if N is a``// Loeschian Number``static` `bool` `isLoeschian(``int` `n)``{``    ` `    ``// Iterate [0, sqrt(N)] for x``    ``for``(``int` `x = 1; x <= Math.Sqrt(n); x++)``    ``{``       ` `       ``// Iterate [0, sqrt(N)] for y``       ``for``(``int` `y = 1; y <= Math.Sqrt(n); y++)``       ``{``           ` `          ``// Check the given criteria``          ``if` `(x * x + x * y + y * y == n)``              ``return` `true``;``       ``}``    ``}` `    ``// If no such pair found then``    ``// return false``    ``return` `false``;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Given Number N``    ``int` `n = 19;` `    ``// Function Call``    ``if` `(isLoeschian(n))``    ``{``        ``Console.WriteLine(``"Yes"``);``    ``}``    ``else``    ``{``        ``Console.WriteLine(``"No"``);``    ``}``}``}` `// This code is contributed by amal kumar choubey`

## Javascript

 ``
Output:
`Yes`

Time Complexity: O(N)

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