1. *** SofaPlay Lite allows unlimited photo and image streaming to your TV, but video streaming is limited to two minutes.
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2. IMPORTANT: SofaPlay Lite is working with devices, which are supporting the UPnP/DLNA Digital Media Renderer standard.
3. Just drag any movie file onto SofaPlay Lite and it will appear instantly on the big screen in front of you.
- IStream allows you to stream your media onto your big TV screen with no configuration at all! Just throw in some files and iStream will do the rest! IStream supports a vast number of media formats and playback devices: From modern SmartTVs via set-top boxes or network-enabled stereos to software solutions (e.g., Kodi or Plex) running on an HTPC, everything is possible.
- SofaPlay streams your media files wirelessly to your TV. Your Mac is completely controlling and managing your TV and taking care of the streaming.
4. SofaPlay Lite allows you to play media files directly from your Mac on the tv.
Browse and download apps for your Mac - from your Mac. Download Pro apps by category, read user reviews, and buy apps in one simple step. If you want to give it a try before you buy, you can download the “lite” version for free and stream anything for up to two minutes. SofaPlay ($5.49) Mac App Store About the Author.
Features and Description
Key Features
Latest Version: 2.1.5
What does SofaPlay Lite do? With Apple TV support: Download SofaPlay TV in the Apple TV App Store to stream music and videos to your Apple TV-----With Xbox One support: Use SofaPlay to stream music and videos to your Xbox One!-----Touch Bar support: SofaPlay now supports the Touch Bar on your new MacBook Pro-----SofaPlay Lite allows you to play media files directly from your Mac on the tv. It connects your Mac to your Smart TV and takes care of the streaming. Just drag any movie file onto SofaPlay Lite and it will appear instantly on the big screen in front of you. SofaPlay Lite streams your video wirelessly to your TV. No configuration needed, no hassle. Just drag and drop. Your Mac is completely controlling and managing your TV and taking care of the streaming. Just lean back on your sofa, get some pop-corn and enjoy a movie, or two. *** SofaPlay Lite allows unlimited photo and image streaming to your TV, but video streaming is limited to two minutes. ***IMPORTANT: SofaPlay Lite is working with devices, which are supporting the UPnP/DLNA Digital Media Renderer standard. Fortunately, most of the new TVs are working with SofaPlay Lite. Also, there are a few supported Blu-Ray Players. If your device has a network connection (wireless or wired), there is a great chance it is supported. Before you download SofaPlay Lite, please use this little app to check if your device is compatible: http://bit.ly/sofaplay-device-check
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[tex]x^2equiv 59(mod 11)[/tex]
I was using Quadratic Residues to determine whether or not my equations had solutions. For example, in the case above, I would write out the quadratic residues of 11:
[tex]QR_{11} = {1,3,4,5,9}[/tex]
Here I noted that if my modulo was prime then the number of quadratic residues is always less than half the prime. So in this case, 11/2 = 5.5 and there are 5 QR's.
Then I would use the Legendre symbol:
[tex](59/11) = (4/11) = 1 quadquadmbox{since 4 is a quadratic residue of 11}[/tex]
Which tells me that my equation has a solution. But notice that I needed to calculate all the quadratic residues first.
So then I came across the Quadratic Reciprocity Law which said that if p and q are primes then
[tex](p/q) = -(q/p)[/tex]
if [itex]p,qequiv 3(mod 4)[/itex], otherwise [itex](p/q) = (q/p)[/itex].
So, this tells me that solving an equation such as [itex]x^2equiv p(mod q)[/itex] is exactly the same as solving [itex]x^2 equiv q(mod p)[/itex], UNLESS p or q is congruent to 3 modulo 4.
EX1. In modulo 5, we have 1 and 4 as quadratic residues. Then (5/97) = (97/5) because neither 5 nor 97 are congruent to 3 modulo 4. So then (5/97) = (97/5) = (2/5) = -1 since 2 is not a QR of 5.
EX2. (85/97) = (5/97)(17/97) {by a corollary of the QRL} = (97/5)(97/17) {since neither 5 nor 17 are congruent to 3 modulo 4} = (2/5)(12/17) {simplifying in mod 17} = (-1)(-1) = 1. Since the QR's of 17 are 1,2,4,8,9,13,15,16, and 12 is not a QR of 17.
My question is: why is what I've written in bold true? Why aren't those two equations equivalent if p or q is congruent to 3 modulo 4? What is so special about 3 modulo 4?