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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite Let $q$ be an odd prime number, such that $p=4q+1$ is also an odd prime. I want to show that the congruence $x^2 equiv -1 pmodp$ has two (incongruenct modulo $p$) solutions, which are quadratic nonresidues modulo $p$. I have thought to consider the Jacobi symbol. We have that $left( frac-1pright)=left( frac-14q+1right)=(-1)^frac4q+1-12=(-1)^2q=1$. From this we deduce that $x^2 equiv -1 pmodp$ has two incongruent modulo $p$ solutions, right? How do we deduce that the solutions are quadratic nonresidues modulo $p$ ? number-theory quadratic-residues share | cite | improve this question asked Aug 6 at 20:09 Evinda 451 4 12 1 Hint: suppose you got quadratic residues. Deduce the existence of an element of order $8$, derive contradiction. – lulu Aug 6 at 20:14 add a comment  |  up vote 0 down vote favorite Let $...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite So as you can see in this photo, i want to express ci (output concentration of mixture) as a function of time. Qi, Cu, K, xv, V - known facts. I know this is an easy work, but my math has become rusty. Problem with expressing ci differential-equations share | cite | improve this question asked Aug 6 at 19:17 user582165 1 Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. – José Carlos Santos Aug 6 at 19:21 add a comment  |  up vote 0 down vote favorite So as you can see in this photo, i want to express ci (output concentration of mixture) as a function of time. Qi, Cu, K, xv, V - known facts. I know this is an easy work, but my math has become rusty. Problem with expressing ci...

Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite This a simple question yet confusing for me, I found the answer as 1220 by taking sum from $11$ to $50$, by inferring the question as first 50 natural numbers $1,2,3,4,5,6,7,8,9,10,11,...49,50$ and sum starting from 11 which means sum $= 11+12+...+49+50$. But my friend says otherwise, he took from 11 to 60 and says answer as 1775. Can anyone explain how to infer the word first in the context of maths. summation word-problem gre-exam natural-numbers share | cite | improve this question edited Aug 6 at 20:26 asked Aug 6 at 18:50 Subhassh Mahenthren 11 3 1 Welcome to MSE. For some basic information about writing mathematics at this site see, e.g. , basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Aug 6 at 18:57 I've fi...