Question

If n = $\frac{a^{2p}-1}{a^2-1}$ where $a$ is an integer $>1$ and $p$ is an odd prime, then $n$ is pseudoprime to the base $a$.

score 67 · Answer 1 · 2026-04-09 03:41:13

67

Views

If n = $\frac{a^{2p}-1}{a^2-1}$ where $a$ is an integer $>1$ and $p$ is an odd prime, then $n$ is pseudoprime to the base $a$.

Published on 09 Apr 2026 - 3:41

score 108 · Answer 2 · 2026-04-09 16:39:01

108

Views

How to find integer solution of a rational function

Published on 09 Apr 2026 - 16:39

score 241 · Answer 3 · 2026-04-15 20:47:30

241

Views

$x^2 \equiv -1$ (mod $p$) has two incongruent solutions given by $x\equiv\pm(\frac{p-1}{2})!$(mod $p$)

Published on 15 Apr 2026 - 20:47

score 587 · Answer 4 · 2026-04-14 17:07:19

587

Views

Show there are infinitely many positive integers $k$ such that $\phi(n)=k$ has exactly two solutions where $n$ is a positive integer

Published on 14 Apr 2026 - 17:07

score 118 · Answer 5 · 2026-04-14 16:01:33

118

Views

Number theory Higher algebra by Bernard and Child

Published on 14 Apr 2026 - 16:01

score 107 · Answer 6 · 2026-04-17 04:18:15

107

Views

Approximate numbers by certains rationals

Published on 17 Apr 2026 - 4:18

score 31 · Answer 7 · 2026-04-14 17:50:15

31

Views

What does $(k!)^2((n-1)!+1)+n(k!-1)(k-1)!\equiv0$ mod $n(n+k)$ reduce/simplify into?

Published on 14 Apr 2026 - 17:50

score 62 · Answer 8 · 2026-04-11 15:54:38

62

Views

Closest power to another power

Published on 11 Apr 2026 - 15:54

score 101 · Answer 9 · 2026-04-14 04:09:18

101

Views

Show that if $n ≥ 5$ then the last $2$ digits in the decimal expansion of $2^{n!}$ are $76$

Published on 14 Apr 2026 - 4:09

score 92 · Answer 10 · 2026-04-12 08:44:38

92

Views

Is $100x^2+20x$ a factorial?

Published on 12 Apr 2026 - 8:44

score 56 · Answer 11 · 2026-04-13 23:03:54

56

Views

How would one find the largest integer $n$ such that $n! < a^n$ for some integer $a$?

Published on 13 Apr 2026 - 23:03

score 28 · Answer 12 · 2026-04-13 22:11:00

28

Views

Probability of an integer factoring "nicely" into exactly two integers smaller than a certain bound.

Published on 13 Apr 2026 - 22:11

score 150 · Answer 13 · 2026-04-15 13:20:41

150

Views

Why does the product of all the elements in $\mathbb{Z} _{m}^{*} $ equal to $\pm {1} \mod{m}$?

Published on 15 Apr 2026 - 13:20

score 365 · Answer 14 · 2026-04-14 16:18:16

365

Views

Prove that $9^n+4^{n+1}$ is a multiple of $5$ for all $n \in \mathbb{N}$

Published on 14 Apr 2026 - 16:18

score 236 · Answer 15 · 2026-04-16 09:38:34

236

Views

$Norm_{(\mathbb Q(\zeta_p)|\mathbb Q)}(1-\zeta_p)=p$

Published on 16 Apr 2026 - 9:38

List Question

If n = $\frac{a^{2p}-1}{a^2-1}$ where $a$ is an integer $>1$ and $p$ is an odd prime, then $n$ is pseudoprime to the base $a$.

How to find integer solution of a rational function

$x^2 \equiv -1$ (mod $p$) has two incongruent solutions given by $x\equiv\pm(\frac{p-1}{2})!$(mod $p$)

Show there are infinitely many positive integers $k$ such that $\phi(n)=k$ has exactly two solutions where $n$ is a positive integer

Number theory Higher algebra by Bernard and Child

Approximate numbers by certains rationals

What does $(k!)^2((n-1)!+1)+n(k!-1)(k-1)!\equiv0$ mod $n(n+k)$ reduce/simplify into?

Closest power to another power

Show that if $n ≥ 5$ then the last $2$ digits in the decimal expansion of $2^{n!}$ are $76$

Is $100x^2+20x$ a factorial?

How would one find the largest integer $n$ such that $n! < a^n$ for some integer $a$?

Probability of an integer factoring "nicely" into exactly two integers smaller than a certain bound.

Why does the product of all the elements in $\mathbb{Z} _{m}^{*} $ equal to $\pm {1} \mod{m}$?

Prove that $9^n+4^{n+1}$ is a multiple of $5$ for all $n \in \mathbb{N}$

$Norm_{(\mathbb Q(\zeta_p)|\mathbb Q)}(1-\zeta_p)=p$

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