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I'm reading Grosswald paper and came across something like this:
enter image description here
and I don't know what exactly does $(-1/p)=+1$ mean, I'm not much into the subject, and I'm not sure whether it's English notation or just something I don't know.
What does this equation $(-1/p)=+1$ mean if said in words? I would be glad to see this as an example.

Kumar
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Satsuki
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    This is the Legendre symbol. $(-1/p) = +1$ means that there is a solution to $x^2 = -1 \pmod{p}$. And $(-1/p) = -1$ means there is not a solution. Most people would read it as "$-1$ is a quadratic residue mod $p$." – B. Goddard May 23 '17 at 18:55

2 Answers2

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That's the Legendre symbol. When $n$ and $p$ are relatively prime $(n/p)$ is $+1$ when $n$ is a square mod $p$, $=1$ otherwise. In this case it means that $-1$ is a quadratic residue of $p$. (That happens just when the odd prime $p$ is congruent to $1$ mod $4$.)

Ethan Bolker
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You can refer this for your examples and all other needful.

https://en.wikipedia.org/wiki/Legendre_symbol

We can see that if there is any perfect square then when it is divided by any prime( preferably odd) then we get ,

$$a^2=Pm,Pm+1,Pm-1$$. Here, $a,p,m\in \mathbb{Z}\mbox{,} p$ is a prime This can be proved by Euclid's division algorithm.

Chandramauli Chakraborty
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