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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.

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  • $\begingroup$ Can you explain it through the numbers and equations because I didn't get how to use these hints thanks $\endgroup$ – Nariman Zendehrooh Nov 12 '17 at 1:06
  • $\begingroup$ Can you please respond $\endgroup$ – Nariman Zendehrooh Nov 13 '17 at 4:09
  • $\begingroup$ @NarimanZendehrooh I gave you all the information you need to solve the problem. Pick first 2040 numbers such that the sum of their squares is a multiple of 4. Then make their sum a difference of two squares. $\endgroup$ – N. S. Nov 13 '17 at 4:55

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