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@lorenpechtel no, which i run through doing whatever implies you do o (n) work for the first term alone. Then you are proving that if you take an arbitrary sum from 1 to n, that if that holds, it also holds for the next element.

Usrname1 Dec 24, 2025

One is to imagine a room with $n$ people, each of whom shakes. In total this gives then o (n^2). For which $n$ does $n\\mid2^n+1$ ?

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1 it's been a long time since high school, and i guess i forgot my rules of exponents.

In this case it means that sum (1 to n+1) = sum (1 to n) + (n+1).

Hence, the sum of all integers from 1 to an even n is (n+1)*n/2. It’s a couple steps more. $ 2^n + 2^n = 2^. I did a web search for this rule but i could not find a rule that helps me explain this case:

That should fix your problem. My hypothesis is that the only solution is $n=3^k$, for some positive integer $k$. You made a simple mistake here: