# Sum of Nth Power in Python

Program to find the number of ways that a given integer can be represented as the sum of the Nth power of the unique, natural numbers. For example, if X = 100 and N = 2, we have to find all combinations of squares adding up to 100. The possible solutions are (100^2), (8^2+6^2), (1^2+3^2+4^2+5^2+7^2). So the total possible solutions are 3.

## Python Program for Sum of Nth Power

def powersum(X, N, num): value = X-pow(num, N) if value<0: # if value is lessthan 0 then there is no solution return 0 elif value==0: # if value is equal 0 then there is excatly one solution return 1 else: # Calculate the number of solution with/ without value return powersum(value, N, num+1)+powersum(X, N, num+1) X = int(input("Enter the value of X: ")) N = int(input("Enter the value of N: ")) print(powersum(X, N, 1))

Output

Enter the value of X: 100 Enter the value of N: 2 3

Enter the value of X: 29 Enter the value of N: 2 2

**Approach**

- Check whether X is equal to 1 power N if so then there is only one possible solution.
- If X is less than 1 power N, then there is no possible solution.
- If X is greater than 1 power N, then return powersum(value, N, num+1)+powersum(X, N, num+1). The first call of powersum includes the 1 power N value and the second call excludes the 1 power N value.

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