query: Proving consecutive quadratic residue modulo p
positive_passages.docid: 17786
positive_passages.text: Existence of Consecutive Quadratic residues
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
negative_passages.docid: 29979
negative_passages.text: When is $-3$ a quadratic residue mod $p$?
negative_passages.docid: 132587
negative_passages.text: Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
negative_passages.docid: 22962
negative_passages.text: How to show $\binom{2p}{p} \equiv 2\pmod p$?
negative_passages.docid: 118955
negative_passages.text: Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus
negative_passages.docid: 52530
negative_passages.text: There exists a prime congruent to $m$ mod $p$
negative_passages.docid: 46147
negative_passages.text: Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
negative_passages.docid: 68635
negative_passages.text: When is $2$ a quadratic residue mod $p$?
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
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: 158863
negative_passages.text: How to prove $\sum_p p^{-2} < \frac{1}{2}$?
negative_passages.docid: 25910
negative_passages.text: Product of Quadratic Residues
negative_passages.docid: 155012
negative_passages.text: Solving quadratic equations in modular arithmetic
negative_passages.docid: 60780
negative_passages.text: Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
negative_passages.docid: 50930
negative_passages.text: Proving the continued fraction representation of $\sqrt{2}$
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion