query: What are the quadratic residues of an odd prime?
positive_passages.docid: 27287
positive_passages.text: $-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
negative_passages.docid: 131731
negative_passages.text: Primes that can't be written as sum of two squares. Mod
negative_passages.docid: 119630
negative_passages.text: For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion
negative_passages.docid: 38498
negative_passages.text: Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
negative_passages.docid: 78379
negative_passages.text: Proof on cubic residues
negative_passages.docid: 54359
negative_passages.text: Odd Primes Problem Proof
negative_passages.docid: 73607
negative_passages.text: Find the residue at $z=-2$ for $g(z) = \frac{\psi(-z)}{(z+1)(z+2)^3}$
negative_passages.docid: 92416
negative_passages.text: About a sum of Legendre symbols associated to an odd prime
negative_passages.docid: 45672
negative_passages.text: Even/Odd Binomial Coefficients
negative_passages.docid: 117516
negative_passages.text: Prime trios of the form $p$,$p+2$,$p+4$
negative_passages.docid: 93898
negative_passages.text: Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
negative_passages.docid: 55621
negative_passages.text: Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
negative_passages.docid: 137230
negative_passages.text: Find all pairs of primes $p,q$ such that $pq \mid 2^p +2^q$
negative_passages.docid: 58182
negative_passages.text: How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
negative_passages.docid: 82808
negative_passages.text: Do there exist any odd prime powers that can be represented as $n^4+4^n$?
negative_passages.docid: 123441
negative_passages.text: Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)