Prove that there does not exist a composite odd number $N > 1$ which does not divide $2^k-1$ for $k = 1,2,\ldots,N-2$.
I conjectured this result, but wasn't sure how to prove it. I tried it for many cases and it seems to be true.
How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...
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