(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]2^{k-1}[/tex] dividesn, while [tex]2^k[/tex] does not. Show that [tex]2^{k-1}[/tex] does not divide [tex]\frac{n(n-1)}{2}[/tex].

3. The attempt at a solution

That [tex]2^{k-1}[/tex] dividesnimplies that [tex]n=2^{k-1}m[/tex], wheremis an integer.

[tex]\frac{n}{2^k}=\frac{m}{2}[/tex], which implies that [tex]2[/tex] does not dividem, which in turn implies that [tex]k\geq 1[/tex].

[tex]\frac{\frac{n(n-1)}{2}}{2^{k-1}}=\frac{m}{2}(n-1)[/tex]

However, the last expression seems like it could still be an integer, given the premises above. Am I missing something?

(Intermediate steps are not shown because I've recalculated them several times and found them to be correct. I'm pretty sure there must be something else that's wrong or missing.)

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# Homework Help: Show that 2^(k-1) doesn't divide n(n-1)/2

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