Question

Can I prove that a solution of $a^2-2b^2=p$ with $1\le b<\sqrt{p}$ always exists?

score 122 · Answer 1 · 2018-05-24 19:39:55

122

Views

Can I prove that a solution of $a^2-2b^2=p$ with $1\le b<\sqrt{p}$ always exists?

Published on 24 May 2018 - 19:39

score 415 · Answer 2 · 2026-03-25 11:54:11

415

Views

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Published on 25 Mar 2026 - 11:54

score 195 · Answer 3 · 2026-02-23 07:43:17

195

Views

Decomposition $2^k$ into a sum of primes

Published on 23 Feb 2026 - 7:43

score 163 · Answer 4 · 2026-03-25 10:24:03

163

Views

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Published on 25 Mar 2026 - 10:24

score 86 · Answer 5 · 2026-03-25 10:25:18

86

Views

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Published on 25 Mar 2026 - 10:25

score 79 · Answer 6 · 2026-03-25 07:43:09

79

Views

The construction of a number with given digits

Published on 25 Mar 2026 - 7:43

score 49 · Answer 7 · 2018-05-25 17:11:09

49

Views

Elementary proof of lower bound for number of squarfree naturals not exceeding $n$

Published on 25 May 2018 - 17:11

score 154 · Answer 8 · 2018-05-25 18:05:43

154

Views

Is there a name for this prime numbers distribution?

Published on 25 May 2018 - 18:05

score 624 · Answer 9 · 2026-03-23 02:51:05

624

Views

How does GIMPS work and what are these iterations?

Published on 23 Mar 2026 - 2:51

score 90 · Answer 10 · 2026-03-23 11:14:37

90

Views

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Published on 23 Mar 2026 - 11:14

score 147 · Answer 11 · 2026-03-26 14:20:30

147

Views

Infinite prime product equals $\sqrt{5}$

Published on 26 Mar 2026 - 14:20

score 176 · Answer 12 · 2026-02-23 07:49:04

176

Views

Lower bound for $g(n)$, the number of decompositions of 2n into ordered sums of two odd primes

Published on 23 Feb 2026 - 7:49

score 76 · Answer 13 · 2018-05-27 02:37:16

76

Views

Property of Prime Counting Function

Published on 27 May 2018 - 2:37

score 382 · Answer 14 · 2026-03-25 13:13:23

382

Views

How many pairs of adjacent numbers each have a prime number of factors?

Published on 25 Mar 2026 - 13:13

score 1.1k · Answer 15 · 2018-05-27 10:25:29

1.1k

Views

Find primes $p$, for which the $x^2 \equiv 7 \pmod{p}$ has a solution

Published on 27 May 2018 - 10:25

List Question

Can I prove that a solution of $a^2-2b^2=p$ with $1\le b<\sqrt{p}$ always exists?

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Decomposition $2^k$ into a sum of primes

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

The construction of a number with given digits

Elementary proof of lower bound for number of squarfree naturals not exceeding $n$

Is there a name for this prime numbers distribution?

How does GIMPS work and what are these iterations?

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Infinite prime product equals $\sqrt{5}$

Lower bound for $g(n)$, the number of decompositions of 2n into ordered sums of two odd primes

Property of Prime Counting Function

How many pairs of adjacent numbers each have a prime number of factors?

Find primes $p$, for which the $x^2 \equiv 7 \pmod{p}$ has a solution

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