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 eibc, ninjaforce, vrondoS, crazylizard, scannose
Hi AOPS community,
We are excited to announce that Westford Academy (located in Westford, MA) will be hosting its first ever math competition for middle school students (grades 5-8).
Based in Massachusetts, this tournament hosts ambitious and mathematically skilled students in grades 5–8 to compete against other middle school math teams while fostering their problem-solving skills and preparing them to continue enriching their STEM skills in high school and in the future.
This competition will be held on April 12, 2025 from 12:00 PM to 5:00 PM and will feature 3 rounds (team, speed, and accuracy). The problems will be of similar difficulty for AMC 8-10 and were written by USA(J)MO and AIME qualifiers.
If you are in the Massachusetts area and are curious about Mathematics, we cordially invite you to sign up by scanning the QR code on the attached flyer. Please note that teams consist of 4-6 competitors, but if you prefer to register as an individual competitor, you will be randomly placed on a team of other individual competitors. Feel free to refer the attached flyer and website as needed.
https://sites.google.com/westfordk12.us/wamt/home?authuser=2
We are excited to announce that Westford Academy (located in Westford, MA) will be hosting its first ever math competition for middle school students (grades 5-8).
Based in Massachusetts, this tournament hosts ambitious and mathematically skilled students in grades 5–8 to compete against other middle school math teams while fostering their problem-solving skills and preparing them to continue enriching their STEM skills in high school and in the future.
This competition will be held on April 12, 2025 from 12:00 PM to 5:00 PM and will feature 3 rounds (team, speed, and accuracy). The problems will be of similar difficulty for AMC 8-10 and were written by USA(J)MO and AIME qualifiers.
If you are in the Massachusetts area and are curious about Mathematics, we cordially invite you to sign up by scanning the QR code on the attached flyer. Please note that teams consist of 4-6 competitors, but if you prefer to register as an individual competitor, you will be randomly placed on a team of other individual competitors. Feel free to refer the attached flyer and website as needed.
https://sites.google.com/westfordk12.us/wamt/home?authuser=2
Attachments:
