Question 1029982
<font face="Times New Roman" size="+2">


2 and 0 are even.  The rest are odd.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(n)\ =\ (-1)^n\ \forall\ n\ \in\ \mathbb{Z}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(n)\ =\ -2(n\ \text{mod}\ 2)\ +\ 1\ \forall\ n\ \in\ \mathbb{Z}]


where *[tex \Large p\ \text{mod}\ q] returns the remainder of the integer quotient of *[tex \Large p] divided by *[tex \Large q].


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>