Determine if there are 2041 distinct natural numbers such that the sum of their squares is a perfect square.
Can anyone please help me to solve this problem?
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Hint Any multiple of $4$ is the difference of two even perfect squares.
Hint 2 You can make the sum of $2040$ perfect squares a multiple of $4$. You can moreover chose the numbers in such a way that they don't repeat and the two numbers in the above hint are not in this set.