perplexus.info :: Just Math : 1+4=5

1+4=5 (Posted on 2016-03-28)

The sum of the squares of the first n positive integers is always a composite number, except the case of n=2.

Prove it.

Submitted by Ady TZIDON

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Solution: (Hide)

Since S=n*(n+1)*(2n+1)/6 - it is easy to see that for n>2 S is composite.

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