Question

On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

score 252 · Answer 1 · 2026-04-14 21:28:28

252

Views

On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

Published on 14 Apr 2026 - 21:28

score 113 · Answer 2 · 2026-04-12 17:18:21

113

Views

How many integral ordered pairs satisfy this equation

Published on 12 Apr 2026 - 17:18

score 84 · Answer 3 · 2026-04-15 21:47:21

84

Views

Evaluating $\cos\frac{k\pi}{p}+\cos\frac{2k\pi}{p}+\cos\frac{3k\pi}{p}+\dots +\cos\frac{2\frac{(p - 1)}{2}k\pi}{p}$

Published on 15 Apr 2026 - 21:47

score 62 · Answer 4 · 2026-04-14 07:24:32

62

Views

How show that the sums equal?

Published on 14 Apr 2026 - 7:24

score 73 · Answer 5 · 2026-04-29 12:47:02

73

Views

Walking positive square numbers and closing or opening doors

Published on 29 Apr 2026 - 12:47

score 210 · Answer 6 · 2026-04-13 10:18:14

210

Views

A variation on Dirichlet's theorem on arithmetic progressions

Published on 13 Apr 2026 - 10:18

score 161 · Answer 7 · 2026-04-09 23:36:03

161

Views

Quartic: Thue equation

Published on 09 Apr 2026 - 23:36

score 1.6k · Answer 8 · 2026-04-29 12:52:13

1.6k

Views

Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?

Published on 29 Apr 2026 - 12:52

score 168 · Answer 9 · 2026-04-16 14:47:35

168

Views

What's equal this:${\frac 12 ^ \frac 13} ^{\cdots \frac1n}$?

Published on 16 Apr 2026 - 14:47

score 195 · Answer 10 · 2026-04-11 18:49:24

195

Views

Proof for a modular arithmetic identity.

Published on 11 Apr 2026 - 18:49

score 105 · Answer 11 · 2026-04-16 03:30:41

105

Views

If $m \ge 2n$, does $\binom{m}{n}$ always have prime factor greater than $n$?

Published on 16 Apr 2026 - 3:30

score 273 · Answer 12 · 2026-04-13 18:06:18

273

Views

Product of $(4k-1)$ primes can't be sum of 2 squares

Published on 13 Apr 2026 - 18:06

score 161 · Answer 13 · 2026-04-29 15:21:22

161

Views

Properties of $v_p(a-b) =n, p$ adic order when $\gcd(a,p)=\gcd(b,p)=1$ about $a^p-b^p$.

Published on 29 Apr 2026 - 15:21

score 440 · Answer 14 · 2026-04-16 05:15:44

440

Views

How to prove $T_{m}T_{n}=\sum_{d|\gcd(m,n)}d^{k-1}T_{mn/d^2}?$ $T_{n}$ is Hecke operator.

Published on 16 Apr 2026 - 5:15

score 69 · Answer 15 · 2026-04-15 00:01:55

69

Views

An explicit ring quotient

Published on 15 Apr 2026 - 0:01

List Question

On the equation $\varphi(n)=\left(\frac{1+\sqrt{1+8n}}{8}\right)\cdot\left(\operatorname{rad}(n)-\frac{1+\sqrt{1+8n}}{2}\right)$

How many integral ordered pairs satisfy this equation

Evaluating $\cos\frac{k\pi}{p}+\cos\frac{2k\pi}{p}+\cos\frac{3k\pi}{p}+\dots +\cos\frac{2\frac{(p - 1)}{2}k\pi}{p}$

How show that the sums equal?

Walking positive square numbers and closing or opening doors

A variation on Dirichlet's theorem on arithmetic progressions

Quartic: Thue equation

Does the sequence $n+\tan(n), n \in\mathbb{N}$ have a lower bound?

What's equal this:${\frac 12 ^ \frac 13} ^{\cdots \frac1n}$?

Proof for a modular arithmetic identity.

If $m \ge 2n$, does $\binom{m}{n}$ always have prime factor greater than $n$?

Product of $(4k-1)$ primes can't be sum of 2 squares

Properties of $v_p(a-b) =n, p$ adic order when $\gcd(a,p)=\gcd(b,p)=1$ about $a^p-b^p$.

How to prove $T_{m}T_{n}=\sum_{d|\gcd(m,n)}d^{k-1}T_{mn/d^2}?$ $T_{n}$ is Hecke operator.

An explicit ring quotient

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