such that 
for all 
.
,
is the greatest prime divisor of 
.
be a nonzero square matrix of order 
satisfying![\[
a_{ik} a_{jk} = a_{kk} a_{ij}, \quad \text{for all } i, j, k.
\]](http://latex.artofproblemsolving.com/7/5/2/752b16a277d9fd18bfda6c3be35d23d42d75ebaa.png)
Denote by 
the trace of 
,
.
be a ring. Let 
such that 
.
is nilpotent, so is 
.
,
,
.
id defined by![\[
f(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
\]](http://latex.artofproblemsolving.com/0/2/c/02c7b4af3cac77da8e3cc102c79a7db2e95f437f.png)
now what is CDF or cumulative distribution function ![$F_X(x)=P[X\leq x]$](http://latex.artofproblemsolving.com/7/9/1/79150c7527581feec873c9c790f8aeddc8f8efb8.png)
![$f(x)\in C[0,3]$](http://latex.artofproblemsolving.com/8/e/2/8e2d8e1cf446975c3e3aa894610ac8b6371737b4.png)
satisfy 
for all 
and
Show that
Y by
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