# Check if given number can be represented as sum of two great numbers

We are given a number N. We need to check if the given number N can be represented as sum of two **Great **numbers. If yes then print those two great numbers else print no. Great numbers are those which are represented in the form : ((b)*(b+1)*(2*b+1))/6 where b is a natural number.

Examples:

Input : N = 35 Output : 5 and 30 Input : 105 Output : 14 and 91 Input : 99 Output : No the given number is not a sum of two great numbers

As we know ((b)*(b+1)*(2*b+1))/6 where b is a natural number represents the sum of square of first b natural numbers. For example if b = 3 then 1+4+9 = 14. So to check if the input number n can be represented as sum of two great numbers then we will first compute all the great numbers less than n in an array. Then we will use two pointer approach to find the pair than can sum up to the given number n.

To compute the array of all the great numbers we will iterate over i=0 to i

Time Complexity: O(N)

Auxiliary Space : O(N)

This article is contributed by **Sanket Singh 2**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**