Question

Proof that if $\sqrt {ab}$ is rational then $\sqrt {\frac{a}{b}}$ is also rational.

score 694 · Answer 1 · 2026-04-28 19:03:56

694

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Proof that if $\sqrt {ab}$ is rational then $\sqrt {\frac{a}{b}}$ is also rational.

Published on 28 Apr 2026 - 19:03

score 108 · Answer 2 · 2026-05-11 09:32:54

108

Views

find the smallest $N$ that $\varphi(n)\ge5$ for every $n\ge N$

Published on 11 May 2026 - 9:32

score 60 · Answer 3 · 2026-05-10 19:35:27

60

Views

proof of Well Ordering Principle over positive integers

Published on 10 May 2026 - 19:35

score 83 · Answer 4 · 2026-04-12 19:06:48

83

Views

How to use modular arithmetic for $a^b-1 $

Published on 12 Apr 2026 - 19:06

score 121 · Answer 5 · 2026-05-15 03:40:46

121

Views

Are there infinitely many primes of the form $k\cdot 2^n+1$ for a fixed $n$ and odd $k$

Published on 15 May 2026 - 3:40

score 281 · Answer 6 · 2026-04-14 18:02:40

281

Views

Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?

Published on 14 Apr 2026 - 18:02

score 935 · Answer 7 · 2026-05-10 16:11:35

935

Views

Can a number be a quadratic residue modulo all prime that do not divide it

Published on 10 May 2026 - 16:11

score 60 · Answer 8 · 2026-05-10 16:16:53

60

Views

Are there any minor extensions of Dirichlet's theorem?

Published on 10 May 2026 - 16:16

score 55 · Answer 9 · 2026-05-10 15:26:13

55

Views

Looking for the name and properties of ${\varphi}_{2} (r, N) = \sum_{- N \le s, t \le N, (r, s, t) = 1} 1$ and $\sum_{d \mid r} \mu (d)/d^2$

Published on 10 May 2026 - 15:26

score 906 · Answer 10 · 2026-04-13 21:49:02

906

Views

What is the remainder when $ n^n $ is divided by $ (n-1) $?

Published on 13 Apr 2026 - 21:49

score 136 · Answer 11 · 2026-04-15 10:52:25

136

Views

If $8x^p+1$ is a square for an odd prime $p$, then $p\mid x-1$

Published on 15 Apr 2026 - 10:52

score 1.7k · Answer 12 · 2026-04-16 19:33:54

1.7k

Views

If $p$ is prime, then $x^2 +5y^2 = p \iff p\equiv 1,9 $ mod $(20)$.

Published on 16 Apr 2026 - 19:33

score 66 · Answer 13 · 2026-04-08 12:23:29

66

Views

Understanding why single-variable expansion of modular arithmetic is valid.

Published on 08 Apr 2026 - 12:23

score 272 · Answer 14 · 2026-04-10 17:49:26

272

Views

Recurring Decimal Expansion

Published on 10 Apr 2026 - 17:49

score 486 · Answer 15 · 2026-05-11 05:19:38

486

Views

Factors in a different base $\ 2b^2\!+\!9b\!+\!7\,\mid\, 7b^2\!+\!9b\!+\!2$

Published on 11 May 2026 - 5:19

List Question

Proof that if $\sqrt {ab}$ is rational then $\sqrt {\frac{a}{b}}$ is also rational.

find the smallest $N$ that $\varphi(n)\ge5$ for every $n\ge N$

proof of Well Ordering Principle over positive integers

How to use modular arithmetic for $a^b-1 $

Are there infinitely many primes of the form $k\cdot 2^n+1$ for a fixed $n$ and odd $k$

Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?

Can a number be a quadratic residue modulo all prime that do not divide it

Are there any minor extensions of Dirichlet's theorem?

Looking for the name and properties of ${\varphi}_{2} (r, N) = \sum_{- N \le s, t \le N, (r, s, t) = 1} 1$ and $\sum_{d \mid r} \mu (d)/d^2$

What is the remainder when $ n^n $ is divided by $ (n-1) $?

If $8x^p+1$ is a square for an odd prime $p$, then $p\mid x-1$

If $p$ is prime, then $x^2 +5y^2 = p \iff p\equiv 1,9 $ mod $(20)$.

Understanding why single-variable expansion of modular arithmetic is valid.

Recurring Decimal Expansion

Factors in a different base $\ 2b^2\!+\!9b\!+\!7\,\mid\, 7b^2\!+\!9b\!+\!2$

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