Is There Only One Integer n That Makes the Sum of Squares a Perfect Square?

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SUMMARY

The discussion confirms that there is only one integer n greater than 1 for which the sum of squares from 1 to n, expressed as 1² + 2² + ... + n² = n(n + 1)(2n + 1)/6, results in a perfect square. This integer is n = 24, where the sum equals 70². The challenge lies in proving that no other integers satisfy this condition.

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elimqiu
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Show that there is only one integer n ( > 1) such that
[URL]http://latex.codecogs.com/gif.latex?1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}[/URL]
is a perfect square
 
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For n = 24, the sum is 70^2
 
It's hard to show that that's the only possible n
 

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