MathDB

41

Part of PEN E Problems

Problems(1)

E 41

Source:

8/6/2011
Show that nn is prime iff
lim⁡r→∞ lim⁡s→∞ lim⁡t→∞ ∑u=0s(1−(cos⁡ (u!)rπn)2t)=n\lim_{r \rightarrow\infty}\,\lim_{s \rightarrow\infty}\,\lim_{t \rightarrow \infty}\,\sum_{u=0}^{s}\left(1-\left(\cos\,\frac{(u!)^{r} \pi}{n} \right)^{2t} \right)=n
PS : I posted it because it's in the PDF file but not here ...
limittrigonometrypen