# Number expressed as sum of five consecutive integers

Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. If yes, find the five consecutive integers, else print “-1”.

Examples:

```Input : n = 15
Output : 1 2 3 4 5
15 = 1 + 2 + 3 + 4 + 5

Input : n = 18
Output : -1
```

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

Method 1: (Brute Force)
The idea is to run a loop from i = 0 to n – 4, check if (i + i+1 + i+2 + i+3 + i+4) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.

Below is the implementation of this approach:

## C++

 `// CPP Program to check if a number can ` `// be expressed as sum of five consecutive ` `// integers. ` `#include ` `using` `namespace` `std; ` ` `  `// function to check if a number can be expressed as ` `// sum of five consecutive integers. ` `void` `checksum(``int` `n) ` `{ ` `    ``// if n is 0 ` `    ``if` `(n == 0) { ` `        ``cout << ``"-2 -1 0 1 2"` `<< endl; ` `        ``return``; ` `    ``} ` ` `  `    ``int` `inc; ` ` `  `    ``// if n is positive, increment loop by 1. ` `    ``if` `(n > 0) ` `        ``inc = 1; ` ` `  `    ``// if n is negative, decrement loop by 1. ` `    ``else` `        ``inc = -1; ` ` `  `    ``// Running loop from 0 to n - 4 ` `    ``for` `(``int` `i = 0; i <= n - 4; i += inc) { ` ` `  `        ``// check if sum of five consecutive ` `        ``// integer is equal to n. ` `        ``if` `(i + i + 1 + i + 2 + i + 3 + i + 4 == n) { ` `            ``cout << i << ``" "` `<< i + 1 ` `                 ``<< ``" "` `<< i + 2 ` `                 ``<< ``" "` `<< i + 3 ` `                 ``<< ``" "` `<< i + 4; ` `            ``return``; ` `        ``} ` `    ``} ` ` `  `    ``cout << ``"-1"``; ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` `    ``int` `n = 15; ` `    ``checksum(n); ` `    ``return` `0; ` `} `

## Java

 `// Java Program to check if a number can ` `// be expressed as sum of five consecutive ` `// integers. ` `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `    ``// function to check if a number can be  ` `    ``// expressed as sum of five consecutive  ` `    ``// integers. ` `    ``static` `void` `checksum(``int` `n) ` `    ``{ ` `        ``// if n is 0 ` `        ``if` `(n == ``0``) { ` `            ``System.out.println(``"-2 -1 0 1 2"``); ` `            ``return``; ` `        ``} ` `     `  `        ``int` `inc; ` `     `  `        ``// if n is positive, increment loop by 1. ` `        ``if` `(n > ``0``) ` `            ``inc = ``1``; ` `     `  `        ``// if n is negative, decrement loop by 1. ` `        ``else` `            ``inc = -``1``; ` `     `  `        ``// Running loop from 0 to n - 4 ` `        ``for` `(``int` `i = ``0``; i <= n - ``4``; i += inc) { ` `     `  `            ``// check if sum of five consecutive ` `            ``// integer is equal to n. ` `            ``if` `(i + i + ``1` `+ i + ``2` `+ i + ``3` `+ i  ` `                                       ``+ ``4` `== n)  ` `            ``{ ` `                ``System.out.print( (i ) ` `                        ``+ ``" "` `+ (i + ``1``) ` `                        ``+ ``" "` `+ (i + ``2``) ` `                        ``+ ``" "` `+ (i + ``3``) ` `                        ``+ ``" "` `+ (i + ``4``)); ` `                ``return``; ` `            ``} ` `        ``} ` `     `  `        ``System.out.println( ``"-1"``); ` `    ``} ` `     `  `    ``// Driver Program ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``int` `n = ``15``; ` `        ``checksum(n); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67 `

## Python3

 `# Python3 code to check if a number ` `# can be expressed as sum of five  ` `# consecutive integers. ` `  `  `# function to check if a number  ` `# can be expressed as sum of five ` `# consecutive integer. ` `def` `checksum(n): ` `  `  `    ``# if n is 0 ` `    ``if` `n ``=``=` `0``: ` `        ``print``(``"-2 -1 0 1 2"``) ` `        ``return` `0` `          `  `    ``inc ``=` `0` `  `  `    ``# if n is positive, ` `    ``# increment loop by 1. ` `    ``if` `n > ``0``: ` `        ``inc ``=` `1` `      `  `    ``# if n is negative, ` `    ``# decrement loop by 1. ` `    ``else``: ` `        ``inc ``=` `-``1` `      `  `    ``# Running loop from 0 to n - 4 ` `    ``for` `i ``in` `range``(``0``, n``-``3``, inc): ` `      `  `        ``# check if sum of five consecutive ` `        ``# integer is equal to n. ` `        ``if` `i ``+` `i ``+` `1` `+` `i ``+` `2` `+` `i ``+` `3` `+` `i ``+` `4` `=``=` `n: ` `            ``print``(i, ``" "``, i ``+` `1``, ``" "``, i ``+` `2``, ``" "``, i ``+` `3``, ``" "``, i ``+` `4``) ` `            ``return` `0` `              `  `    ``print``(``"-1"``) ` `      `  `# Driver Code  ` `n ``=` `15` `checksum(n) `

## C#

 `// C# Program to check if a number can ` `// be expressed as sum of five consecutive ` `// integers. ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// function to check if a number can be  ` `    ``// expressed as sum of five consecutive  ` `    ``// integers. ` `    ``static` `void` `checksum(``int` `n) ` `    ``{ ` `        ``// if n is 0 ` `        ``if` `(n == 0) { ` `            ``Console.Write(``"-2 -1 0 1 2"``); ` `            ``return``; ` `        ``} ` `     `  `        ``int` `inc; ` `     `  `        ``// if n is positive, increment loop by 1. ` `        ``if` `(n > 0) ` `            ``inc = 1; ` `     `  `        ``// if n is negative, decrement loop by 1. ` `        ``else` `            ``inc = -1; ` `     `  `        ``// Running loop from 0 to n - 4 ` `        ``for` `(``int` `i = 0; i <= n - 4; i += inc) { ` `     `  `            ``// check if sum of five consecutive ` `            ``// integer is equal to n. ` `            ``if` `(i + i + 1 + i + 2 + i + 3 + i  ` `                                    ``+ 4 == n)  ` `            ``{ ` `                ``Console.Write( (i ) ` `                        ``+ ``" "` `+ (i + 1) ` `                        ``+ ``" "` `+ (i + 2) ` `                        ``+ ``" "` `+ (i + 3) ` `                        ``+ ``" "` `+ (i + 4)); ` `                ``return``; ` `            ``} ` `        ``} ` `     `  `        ``Console.WriteLine( ``"-1"``); ` `    ``} ` `     `  `    ``// Driver Program ` `    ``public` `static` `void` `Main ()  ` `    ``{ ` `        ``int` `n = 15; ` `        ``checksum(n); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67 `

## PHP

 ` 0) ` `        ``\$inc` `= 1; ` ` `  `    ``// if n is negative, ` `    ``// decrement loop by 1. ` `    ``else` `        ``\$inc` `= -1; ` ` `  `    ``// Running loop from ` `    ``// 0 to n - 4 ` `    ``for` `(``\$i` `= 0;  ` `         ``\$i` `<= ``\$n` `- 4; ``\$i` `+= ``\$inc``)  ` `    ``{ ` ` `  `        ``// check if sum of five  ` `        ``// consecutive integer  ` `        ``// is equal to n. ` `        ``if` `(``\$i` `+ ``\$i` `+ 1 + ``\$i` `+ 2 +  ` `            ``\$i` `+ 3 + ``\$i` `+ 4 == ``\$n``)  ` `        ``{ ` `            ``echo` `\$i` `, ``" "` `, ``\$i` `+ 1, ` `                      ``" "` `, ``\$i` `+ 2, ` `                      ``" "` `, ``\$i` `+ 3, ` `                      ``" "` `, ``\$i` `+ 4; ` `            ``return``; ` `        ``} ` `    ``} ` ` `  `    ``echo` `"-1"``; ` `} ` ` `  `// Driver Code ` `\$n` `= 15; ` `checksum(``\$n``); ` ` `  `// This code is contributed ` `// by ajit ` `?> `

Output :

```1 2 3 4 5
```

Method 2: (Efficient Approach)
The idea is to check if n is multiple of 5 or not.
Let n is sum of three consecutive integer of k – 2, k-1, k, k + 1, k+2. Therefore,
k-2 + k-1 + k + k+1 + k+2= n
5*k = n
The three number will be n/5 – 2, n/5 – 1, n/5, n/5 + 1, n/5 + 2.

Below is the implementation of this approach:

## C++

 `// CPP Program to check if a number can be ` `// expressed as sum of five consecutive integer. ` `#include ` `using` `namespace` `std; ` ` `  `// function to check if a number can be ` `// expressed as sum of five consecutive ` `// integers. ` `void` `checksum(``int` `n) ` `{ ` `    ``// if n is multiple of 5 ` `    ``if` `(n % 5 == 0) ` `        ``cout << n / 5 - 2 << ``" "` `             ``<< n / 5 - 1 << ``" "` `<< n / 5 ` `             ``<< ``" "` `<< n / 5 + 1 << ``" "` `             ``<< n / 5 + 2; ` ` `  `    ``// else print "-1". ` `    ``else` `        ``cout << ``"-1"``; ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` `    ``int` `n = 15; ` `    ``checksum(n); ` `    ``return` `0; ` `} `

## Java

 `// Java Program to check if a number can ` `// be expressed as sum of five consecutive ` `// integer. ` `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `    ``// function to check if a number can ` `    ``// be expressed as sum of five  ` `    ``// consecutive integers. ` `    ``static` `void` `checksum(``int` `n) ` `    ``{ ` `        ``// if n is multiple of 5 ` `        ``if` `(n % ``5` `== ``0``) ` `            ``System.out.println( (n / ``5` `- ``2``) ` `                  ``+ ``" "` `+ (n / ``5` `- ``1``) + ``" "` `                  ``+ (n / ``5``) + ``" "` `+ (n / ``5`  `                ``+ ``1` `) + ``" "` `+ (n / ``5` `+ ``2``)); ` `     `  `        ``// else print "-1". ` `        ``else` `            ``System.out.println( ``"-1"``); ` `    ``} ` `     `  `    ``// Driver Program ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `n = ``15``; ` `        ``checksum(n); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## Python3

 `# Python3 code to check if a number  ` `# can be expressed as sum of five ` `# consecutive integer. ` `  `  `# function to check if a number  ` `# can be expressed as sum of five ` `# consecutive integers. ` `def` `checksum(n): ` `    ``n ``=` `int``(n) ` `      `  `    ``# if n is multiple of 5 ` `    ``if` `n ``%` `5` `=``=` `0``: ` `        ``print``(``int``(n ``/` `5` `-` `2``), ``" "``, ` `         ``int``(n ``/` `5` `-` `1``), ``" "``, ``int``(n ``/` `5``), ``" "``, ``int``(n ``/` `5` `+` `1``), ``" "``, ``int``(n ``/` `5` `+` `2``)) ` `      `  `    ``# else print "-1". ` `    ``else``: ` `        ``print``(``"-1"``) ` `          `  `# Driver Code ` `n ``=` `15` `checksum(n) `

## C#

 `// C# Program to check if a number can ` `// be expressed as sum of five consecutive ` `// integer. ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// function to check if a number can ` `    ``// be expressed as sum of five  ` `    ``// consecutive integers. ` `    ``static` `void` `checksum(``int` `n) ` `    ``{ ` `        ``// if n is multiple of 5 ` `        ``if` `(n % 5 == 0) ` `            ``Console.WriteLine( (n / 5 - 2) ` `                ``+ ``" "` `+ (n / 5 - 1) + ``" "` `                ``+ (n / 5) + ``" "` `+ (n / 5 ` `                ``+ 1 ) + ``" "` `+ (n / 5 + 2)); ` `     `  `        ``// else print "-1". ` `        ``else` `            ``Console.WriteLine( ``"-1"``); ` `    ``} ` `     `  `    ``// Driver Program ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `n = 15; ` `        ``checksum(n); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## PHP

 ` `

Output:

```1 2 3 4 5
```

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