Question

Can a parallelogram have whole-number lengths for all four sides and both diagonals?

score 2.1k · Answer 1 · 2026-04-12 10:50:13

2.1k

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Can a parallelogram have whole-number lengths for all four sides and both diagonals?

Published on 12 Apr 2026 - 10:50

score 408 · Answer 2 · 2026-03-25 04:43:47

408

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$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Published on 25 Mar 2026 - 4:43

score 260 · Answer 3 · 2018-02-28 18:58:25

260

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Generalization of the Armstrong-like and related numbers

Published on 28 Feb 2018 - 18:58

score 104 · Answer 4 · 2026-03-25 01:21:54

104

Views

Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

Published on 25 Mar 2026 - 1:21

score 78 · Answer 5 · 2018-02-28 19:22:56

78

Views

How to prove $\log\left(\frac e{2t}\right) \approx \log\left(\frac1t\right)$ for $0 < t < \frac 12$?

Published on 28 Feb 2018 - 19:22

score 960 · Answer 6 · 2026-04-12 17:08:06

960

Views

Linear congruential generator maximum cycle length.

Published on 12 Apr 2026 - 17:08

score 132 · Answer 7 · 2026-04-12 16:59:46

132

Views

Find a primitive root of (a) $U(\mathbb{Z}/121\mathbb{Z})$, and (b) $U(\mathbb{Z}/18\mathbb{Z})$

Published on 12 Apr 2026 - 16:59

score 55 · Answer 8 · 2018-03-01 00:32:38

55

Views

Prove: For $m,n,a \in \mathbb{Z+}$, if $m \gt n$, then $a^{2^n} +1 \mid a^{2^m} -1$

Published on 01 Mar 2018 - 0:32

score 1.2k · Answer 9 · 2026-04-11 18:29:02

1.2k

Views

Strange Pattern in Decimal Expansion

Published on 11 Apr 2026 - 18:29

score 795 · Answer 10 · 2026-03-25 14:22:57

795

Views

Find the inverse of $8$ modulo $27$

Published on 25 Mar 2026 - 14:22

score 364 · Answer 11 · 2026-04-10 20:35:49

364

Views

Strong vs weak induction on an example from number theory

Published on 10 Apr 2026 - 20:35

score 3.1k · Answer 12 · 2026-03-25 01:17:08

3.1k

Views

Numbers up to 1000 divisible by 2 or 3 and no other prime

Published on 25 Mar 2026 - 1:17

score 89 · Answer 13 · 2026-03-27 23:23:17

89

Views

Complete the following proof by contradiction

Published on 27 Mar 2026 - 23:23

score 283 · Answer 14 · 2018-03-01 19:19:45

283

Views

Number of digits in $2^{1989} $and $5^{1989}$

Published on 01 Mar 2018 - 19:19

score 4.1k · Answer 15 · 2026-03-25 21:50:04

4.1k

Views

Prove that there are infinitely many primes of the form $6n + 5$

Published on 25 Mar 2026 - 21:50

List Question

Can a parallelogram have whole-number lengths for all four sides and both diagonals?

$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Generalization of the Armstrong-like and related numbers

Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

How to prove $\log\left(\frac e{2t}\right) \approx \log\left(\frac1t\right)$ for $0 < t < \frac 12$?

Linear congruential generator maximum cycle length.

Find a primitive root of (a) $U(\mathbb{Z}/121\mathbb{Z})$, and (b) $U(\mathbb{Z}/18\mathbb{Z})$

Prove: For $m,n,a \in \mathbb{Z+}$, if $m \gt n$, then $a^{2^n} +1 \mid a^{2^m} -1$

Strange Pattern in Decimal Expansion

Find the inverse of $8$ modulo $27$

Strong vs weak induction on an example from number theory

Numbers up to 1000 divisible by 2 or 3 and no other prime

Complete the following proof by contradiction

Number of digits in $2^{1989} $and $5^{1989}$

Prove that there are infinitely many primes of the form $6n + 5$

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