Question

Sum of two squares
First, you are given an integer X. You determined the number of ways that you can represent the integer X as the sum of two squares
Now, you represent the number X as the product of N numbers.
If you are given a number N, then represent the product of these N numbers as the sum of two squares.
Input format
• First line: Single integer N denoting the numbers
. Next line: space-separated integers denoting the values of the
numbers
Output format
Output the number of ways of representing the number X as the sum of two squares, where X is the product of N numbers.
Note: Number of ways of representing a number X as sum of two squares can be very large, so output the answer modulo 10' + 7.
Constraints
1<N<200
1<x< 102000
Note: None of the numbers exceed 100
Sample Input
3
2 1 2
Sample Output
4​

Answer 1

Language used : Python Programming

Note : Probably, the question should the like product of two squares should be the product of n numbers, as the sum of them is not qualifying the test case you have given.

given numbers [2,1,2] => product = 2*1*2 = 4

Sum of squares of 2 numbers = 2**2 + 1**2 = 4+1 = 5 atleast. So, the output will be zero if we sum up.

If we go for product of squares, the permutations [2,1], [1,2], [2,1], [1,2] are the four possibilities that gives product 4 as answer.

Program :

from itertools import permutations

n=int(input())

prod=1

count=0

x=list(input().split())

if len(x)==n:

   for i in x:

       prod=prod*int(i)

       if int(i)>100:

           print("Number exceeds 100")

           quit()

   y=permutations(x,2)

   for i in y:

       if (int(i[0])**2 * int(i[1])**2) == prod :

           count=count+1

print(count)

Input :

3

2 1 2

Output :

4

Explanation :

• Take the number of numbers to be considered as input and read them, list them out.

• Check if any of them are >100, if yes, stop the program there.

• Else, list out all the 2 ranged permutations and check each permutations multiplication of squares of the each of two elements in it.

• If it equals the product, increment count by 1.

• Repeat the same process, till all the permutations are checked.

• Once the loop terminates, print the count. That's it!

Learn more :

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3) Write a Python function sumsquare(l) that takes a nonempty list of integers and returns a list [odd,even], where odd is the sum of squares all the odd numbers in l and even is the sum of squares of all the even numbers in l.

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