R 2017: Fill & Download for Free

1008Wilson's Theorem says for a prime number 'p'Rem [ (p-1)! / p] = p-1This can be extended to say,Rem [ (p-2)! / p] = 12017 is a prime number.=> Rem [2015! / 2017] = 1=> Rem [2015*2014! / 2017] = 1=> Rem [(-2)*r / 2017] = 1=> -2r = 2017k + 1If we put k = 1, we get r = -(2017 + 1)/2 = -1009So, if our remainder r = -1009This is the same as getting a remainder of -1009 + 2017 = 1008So, the remainder when 2014! is divided by 2017 is 1008.I have solved a bunch of similar questions on Quora and complied them in one place on by blog here: Remainders (Quantitative Aptitude) for CAT Exam Preparation – Free PDF for Download

The AK could, realistically, remain the weapon of choice for terrorists and the such until new technology exists that makes them too outdated. However here’s a few rifles that might become the staple of Anti-Humanity endeavours.G36- A German rifle that’s about to go out of styleFAL - Once the AK craze passes, it might be seen even moreAUG - pretty much every nation that uses this right now wants to get rid of itAR15/m16/m4 -Terrorism never ends, and eventually we’re going end up with enough of our guns in their hands that it becomes the normSA-80 - the bullpup fad is beginning to break, and HK, who makes the gun, It pushing more for their HK416AK-101 - The 47 might fade out, but it’s grandkids won’tIWI Tavor - Yet another rifle being left behind with the Bullpup craze.OA-R-2017-A1 - Just a bit of wishful thinking for those whom follow my gunsmithing career. Maybe one day long after I’m dead my rifle will be bastardized by terrorists. Who knows? [no picture because I haven’t patented the design yet]Terrorism doesn’t just belong to one nation. It’s global, so some of these are already the chosen rifle of terrorists, and others are getting close to being the chosen rifle of terrorists.

Note that the function [math]f[/math] satisfies-[math]\displaystyle f(x) + f(1-x) = 1 \tag{1}[/math]Also note that the given sum can be rewritten as-[math]\displaystyle S= \left( f \left( \frac{1}{2017} \right) + f \left(1- \frac{1}{2017} \right) \right) + \left( f \left( \frac{2}{2017} \right) + f \left(1- \frac{2}{2017} \right) \right)+ \ldots \tag*{}[/math]Which in a more compact form is-[math]\displaystyle S = \sum_{r=1}^{1008} \left( f \left( \frac{r}{2017} \right) + f \left(1- \frac{r}{2017} \right) \right) \tag*{}[/math]We now apply the property of [math]f[/math] in [math](1) [/math] to obtain-[math]\displaystyle S = \sum_{r=1}^{1008}(1) = 1008 \tag*{}[/math]