I need to prove that -1 is a quadratic residue of an odd prime p iff p = 1 (mod 4)  Any Ideas? Thanks
I came across this problem and I believe Lagrange's theorem is the key to its solution.  The question is:     Let $p$ be an odd prime. Prove that there is some integer $x$ such that $x^2 \equiv −1 \pmod p$ if and only if $p \equiv 1 \pmod 4$.   I appreciate any help.  Thanks.
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This is my idea:    Calculate Avarage for all my points  Move my Camera "up" to correctly "frame" all my points  (i don't know how) Use Unity LookAt(myAvaragePoint)   Thanks Specifing ip address for outbound connections on a multi ip host one of my servers (Debian 5.0.6) has two public ip-address on the same interface. This used to work well for months but suddenly it is using "the wrong" ip addresses for outgoing connections. This is a problem because the reverse lookup will not match and emails therefore get spam points.  eth0      Link encap:Ethernet  Hardware Adresse 00:1b:21:14:8e:9c             inet Adresse:81.169.180.51  Bcast:81.169.180.51  Maske:255.255.255.255           inet6-Adresse: fe80::21b:21ff:fe14:8e9c/64 Gültigkeitsbereich:Verbindung  eth0:0    Link encap:Ethernet  Hardware Adresse 00:1b:21:14:8e:9c             inet Adresse:85.214.157.120  Bcast:85.214.157.120  Maske:255.255.255.255   Kernel-IP-Routentabelle Destination     Router          Genmask         Flags Metric Ref    Use Iface 81.169.180.1    0.0.0.0         255.255.255.255 UH    0      0        0 eth0 0.0.0.0         81.169.180.1    0.0.0.0         UG    0      0        0 eth0   Currently it is using 85.214.157.120 for outbound connections. How do I get it to use 81.169.180.51?  Edit: The netmask of 255.255.255.255 is consistent with both documentation and DHCP response of the hosting company. Calling /etc/init.d/networking restart multiple times will eventually end up with the correct ip-address for outbount connections. But that is obviously not a stable solution. /Edit  Edit 2: To make sure that the host route is not related to my issue, I setup a local test network:  eth0      inet Adresse:192.168.0.2  Bcast:192.168.0.255  Maske:255.255.255.0 eth0:0    inet Adresse:192.168.0.3  Bcast:192.168.0.255  Maske:255.255.255.0  192.168.0.0    0.0.0.0         255.255.255.0   U     0      0        0 eth0 0.0.0.0        192.168.0.1     0.0.0.0         UG    0      0        0 eth0   If anyone has an idea how to make sure that source ip-address 192.168.0.2 is used on outbound tcp connections, I'd be thankful. /Edit 2 Force pagebreak after every sentence/paragraph Is there a way to force a pagebreak after every sentence or paragraph?  This may seem like an odd thing to do, but for catching typos and just general editing I find it much easier to look at a sentence or paragraph in isolation so that I am not tempted to skip ahead.  Currently, I just zoom in so I can only see a few word at a time, but this is not a perfect solution. Effect of switching response and explanatory variable in simple linear regression Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly generate data from that R code: x &lt;- 1:100; y &lt;- ax + b + rnorm(length(x)) and then fit a model like y ~ x, I obviously get reasonably good estimates for $a$ and $b$.  If I switch the role of the variables as in (x ~ y), however, and then rewrite the result for $y$ to be a function of $x$, the resulting slope is always steeper (either more negative or more positive) than that estimated by the y ~ x regression. 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