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# Maybe IMO should give this out

Prove that there does exist some integers $$n$$ such that $$3^{n}+3^{n-1}+3^{n-2}+......+3^{4}+3^{3}+3^{2}+3^{1}+3^{0}$$ is a perfect square, or else define the $\color{BLUE}{\huge{1000th}}$ smallest value of $$n$$.

Note by Bryan Lee Shi Yang
2 years, 10 months ago

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...Sorry, note edited.

- 2 years, 10 months ago

You have mentioned it to be an integer. Other values will be 0,1,4

- 2 years, 10 months ago

I am sorry, it should be a $$POSITIVE$$ number.

- 2 years, 10 months ago

It can be a perfect square. Smallest possible value of n will be -1.

- 2 years, 10 months ago