Question

If p is a prime with p > 5, then 5 is a quadratic residue modulo p if and only if the last decimal digit of p is 1 or 9.

score 1.5k · Answer 1 · 2026-03-25 23:58:40

1.5k

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If p is a prime with p > 5, then 5 is a quadratic residue modulo p if and only if the last decimal digit of p is 1 or 9.

Published on 25 Mar 2026 - 23:58

score 148 · Answer 2 · 2016-04-14 00:31:49

148

Views

For which odd primes $p ≠ 5$ is 10 a qudratic residue modulo $p$?

Published on 14 Apr 2016 - 0:31

score 151 · Answer 3 · 2016-04-19 03:01:01

151

Views

Without using prime factorization, find a prime factor of $\frac{(3^{41} -1)}{2}$

Published on 19 Apr 2016 - 3:01

score 63 · Answer 4 · 2026-03-25 23:58:40

63

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let $q$ be a prime of the form $q=3r+1$ and assume that $p=4q+1$ is also a prime. Show that $3$ is a primitive root of $p$

Published on 25 Mar 2026 - 23:58

score 229 · Answer 5 · 2026-03-26 13:01:08

229

Views

How do you evaluate the quadratic residue of 7 mod p?

Published on 26 Mar 2026 - 13:01

score 96 · Answer 6 · 2016-04-25 08:27:11

96

Views

Question about the solutions to quadratic congruence $x^2\equiv -1(\mbox{mod}\;p)$

Published on 25 Apr 2016 - 8:27

score 1.1k · Answer 7 · 2016-04-26 23:24:47

1.1k

Views

How to find a square root mod $pq$ given that $p \equiv q \equiv 3 \pmod 4$

Published on 26 Apr 2016 - 23:24

score 165 · Answer 8 · 2016-04-29 13:54:35

165

Views

Is it always true, for a prime $p$, a generator $g$ of $\mathbb{Z}^*_p$ cannot be a quadratic residue modulo $p$?

Published on 29 Apr 2016 - 13:54

score 94 · Answer 9 · 2016-04-30 13:28:27

94

Views

Looking for a simpler solution about quadratic congruence

Published on 30 Apr 2016 - 13:28

score 74 · Answer 10 · 2016-05-02 15:09:51

74

Views

If $a\not\equiv 0\mod{p}$ then there are $p-1$ solutions (ordered pairs) to $x^2-y^2\equiv a\mod{p}$

Published on 02 May 2016 - 15:09

score 3k · Answer 11 · 2016-05-03 05:59:10

3k

Views

Number of solutions to $x^2\equiv b \mod p^n$

Published on 03 May 2016 - 5:59

score 91 · Answer 12 · 2016-05-03 18:23:36

91

Views

Difference between a quadratic residue and a number is a quadratic residue

Published on 03 May 2016 - 18:23

score 46 · Answer 13 · 2016-05-05 18:46:57

46

Views

Let $N=3^{1000}\times 2^{200009} +1$. Show that $5^{\frac{N-1}{2}}\equiv -1 \pmod{N}$.

Published on 05 May 2016 - 18:46

score 52 · Answer 14 · 2016-05-10 20:35:49

52

Views

Using the Law Quadratic Residues

Published on 10 May 2016 - 20:35

score 3.9k · Answer 15 · 2016-05-11 14:24:42

3.9k

Views

$x^{2} \equiv-1\ \pmod p$ has a solution if and only if $p\equiv 1\ \pmod 4$

Published on 11 May 2016 - 14:24

List Question

If p is a prime with p > 5, then 5 is a quadratic residue modulo p if and only if the last decimal digit of p is 1 or 9.

For which odd primes $p ≠ 5$ is 10 a qudratic residue modulo $p$?

Without using prime factorization, find a prime factor of $\frac{(3^{41} -1)}{2}$

let $q$ be a prime of the form $q=3r+1$ and assume that $p=4q+1$ is also a prime. Show that $3$ is a primitive root of $p$

How do you evaluate the quadratic residue of 7 mod p?

Question about the solutions to quadratic congruence $x^2\equiv -1(\mbox{mod}\;p)$

How to find a square root mod $pq$ given that $p \equiv q \equiv 3 \pmod 4$

Is it always true, for a prime $p$, a generator $g$ of $\mathbb{Z}^*_p$ cannot be a quadratic residue modulo $p$?

Looking for a simpler solution about quadratic congruence

If $a\not\equiv 0\mod{p}$ then there are $p-1$ solutions (ordered pairs) to $x^2-y^2\equiv a\mod{p}$

Number of solutions to $x^2\equiv b \mod p^n$

Difference between a quadratic residue and a number is a quadratic residue

Let $N=3^{1000}\times 2^{200009} +1$. Show that $5^{\frac{N-1}{2}}\equiv -1 \pmod{N}$.

Using the Law Quadratic Residues

$x^{2} \equiv-1\ \pmod p$ has a solution if and only if $p\equiv 1\ \pmod 4$

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