List questions from quadratic-residues

Published on 28 Apr 2015 - 0:06

660

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Proof that every quadratic residue has two roots, modulo a prime

Published on 28 Apr 2015 - 6:33

136

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Given $x\equiv b^{(2p-1)/3} \pmod{p}$, show that $x^{3} \equiv b \pmod{p}$.

Published on 30 Apr 2015 - 7:58

802

Views

Find all primes $p$ such that $\left( \frac{-19}{p} \right) = 1$

Published on 25 Mar 2026 - 16:13

83

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Find conditions for $\left(\frac{-3}{p}\right)=1$

Published on 25 Mar 2026 - 16:13

850

Views

Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

Published on 01 May 2015 - 17:38

409

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If $ p $ is an odd prime and $ D $ an integer not divisible by $ p $, show that $ x^2 - y^2 \equiv D ~ (\text{mod} ~ p) $ has $ (p - 1) $ solutions.

Published on 03 May 2015 - 16:15

1.1k

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Find the set of primes p for which -3 is quadratic residue mod p

Published on 25 Mar 2026 - 22:05

1.9k

Views

Proving consecutive quadratic residue modulo p

Published on 04 May 2015 - 22:19

1k

Views

Find pseudo-square mod $n$

Published on 23 Feb 2026 - 4:34

649

Views

Describe the set of odd primes such that $\left(\frac{-5}{p}\right) = 1$ (Legendre Symbol)

Published on 25 Mar 2026 - 16:13

184

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For a prime $p\ge 17$ is $\dfrac{p^2-1}{24}$ ever a prime?

Published on 09 May 2015 - 13:42

8.4k

Views

When is $2$ a quadratic residue mod $p$?

Published on 25 Mar 2026 - 17:51

914

Views

Number Theory - Sum of Squares and Quadratic Residue

Published on 10 May 2015 - 3:34

174

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Sequence of perfect squares

Published on 18 May 2015 - 18:45

List Question

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Proof that every quadratic residue has two roots, modulo a prime

Given $x\equiv b^{(2p-1)/3} \pmod{p}$, show that $x^{3} \equiv b \pmod{p}$.

Find all primes $p$ such that $\left( \frac{-19}{p} \right) = 1$

Find conditions for $\left(\frac{-3}{p}\right)=1$

Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

If $ p $ is an odd prime and $ D $ an integer not divisible by $ p $, show that $ x^2 - y^2 \equiv D ~ (\text{mod} ~ p) $ has $ (p - 1) $ solutions.

Find the set of primes p for which -3 is quadratic residue mod p

Proving consecutive quadratic residue modulo p

Find pseudo-square mod $n$

Describe the set of odd primes such that $\left(\frac{-5}{p}\right) = 1$ (Legendre Symbol)

For a prime $p\ge 17$ is $\dfrac{p^2-1}{24}$ ever a prime?

When is $2$ a quadratic residue mod $p$?

Number Theory - Sum of Squares and Quadratic Residue

Sequence of perfect squares

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