Question

For primes $p,q$ one has $2p^2=q^2 + 1$. $p=5$ and $q=7 $ are solutions. Any others?

score 108 · Answer 1 · 2018-07-19 17:46:17

108

Views

For primes $p,q$ one has $2p^2=q^2 + 1$. $p=5$ and $q=7 $ are solutions. Any others?

Published on 19 Jul 2018 - 17:46

score 360 · Answer 2 · 2026-02-23 07:48:07

360

Views

Every integer greater than $0$ can be expressed as a sum of $a$'s and $b$'s, if and only if $a$ and $b$ have no common factor

Published on 23 Feb 2026 - 7:48

score 106 · Answer 3 · 2018-07-22 15:09:45

106

Views

If $\min\{x \in\mathbb{N} : xn+1 \text{ is a square}\} \geq \frac{n}{4}$ then n is prime.

Published on 22 Jul 2018 - 15:09

score 81 · Answer 4 · 2018-07-22 23:20:31

81

Views

How do you find the number of primes in a sequence up to the first thousand terms?

Published on 22 Jul 2018 - 23:20

score 786 · Answer 5 · 2018-07-24 00:42:17

786

Views

Why don’t mathematicians work on ‘difference-asymptotic’ of prime counting function?

Published on 24 Jul 2018 - 0:42

score 139 · Answer 6 · 2026-03-28 09:45:44

139

Views

Prove that the equation: ${a^k + b^k \equiv c^k}\mod{p}$ has no solutions under the following conditions

Published on 28 Mar 2026 - 9:45

score 472 · Answer 7 · 2018-07-24 15:53:15

472

Views

Find number of ordered pairs

Published on 24 Jul 2018 - 15:53

score 240 · Answer 8 · 2018-07-24 21:41:43

240

Views

Show that if $p_1^4 + \cdots + p_{31}^4$ is divisible by $30$, then three consecutive primes are included

Published on 24 Jul 2018 - 21:41

score 135 · Answer 9 · 2018-07-25 16:31:44

135

Views

Proof that every arithmetic progression which might contain a prime does so.

Published on 25 Jul 2018 - 16:31

score 84 · Answer 10 · 2026-03-25 21:01:38

84

Views

How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

Published on 25 Mar 2026 - 21:01

score 199 · Answer 11 · 2026-03-25 17:19:43

199

Views

Are there further primes of the form $\varphi(n)^{\varphi(\varphi(n))}+1$?

Published on 25 Mar 2026 - 17:19

score 312 · Answer 12 · 2026-03-25 20:35:03

312

Views

Does this qualify as a prime-representing Diophantine equation?

Published on 25 Mar 2026 - 20:35

score 70 · Answer 13 · 2026-03-25 07:16:35

70

Views

How to evaluate $ \prod_{1\le i <j\le\frac{p-1}{2}}j^2-i^2 \pmod p$

Published on 25 Mar 2026 - 7:16

score 53 · Answer 14 · 2026-03-28 09:45:47

53

Views

$1 + b^n \equiv c^n \pmod p$ find values of $n$ in $(0,p)$

Published on 28 Mar 2026 - 9:45

score 118 · Answer 15 · 2018-07-27 17:56:27

118

Views

Root 2 primes make up 38% of all prime numbers.

Published on 27 Jul 2018 - 17:56

List Question

For primes $p,q$ one has $2p^2=q^2 + 1$. $p=5$ and $q=7 $ are solutions. Any others?

Every integer greater than $0$ can be expressed as a sum of $a$'s and $b$'s, if and only if $a$ and $b$ have no common factor

If $\min\{x \in\mathbb{N} : xn+1 \text{ is a square}\} \geq \frac{n}{4}$ then n is prime.

How do you find the number of primes in a sequence up to the first thousand terms?

Why don’t mathematicians work on ‘difference-asymptotic’ of prime counting function?

Prove that the equation: ${a^k + b^k \equiv c^k}\mod{p}$ has no solutions under the following conditions

Find number of ordered pairs

Show that if $p_1^4 + \cdots + p_{31}^4$ is divisible by $30$, then three consecutive primes are included

Proof that every arithmetic progression which might contain a prime does so.

How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

Are there further primes of the form $\varphi(n)^{\varphi(\varphi(n))}+1$?

Does this qualify as a prime-representing Diophantine equation?

How to evaluate $ \prod_{1\le i <j\le\frac{p-1}{2}}j^2-i^2 \pmod p$

$1 + b^n \equiv c^n \pmod p$ find values of $n$ in $(0,p)$

Root 2 primes make up 38% of all prime numbers.

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