Question

If $\frac{x^2}{4}$ is an integer greater than 50, then what is the smallest possible value of $x^2$

score 125 · Answer 1 · 2026-04-17 01:04:23

125

Views

If $\frac{x^2}{4}$ is an integer greater than 50, then what is the smallest possible value of $x^2$

Published on 17 Apr 2026 - 1:04

score 221 · Answer 2 · 2026-05-10 15:52:31

221

Views

How to solve this radical expression: $\frac 1{xy} \times (\sqrt{xy} - \frac{xy}{x-\sqrt{xy}})\times (\sqrt{xy} + \frac{xy}{x+\sqrt{xy}})$

Published on 10 May 2026 - 15:52

score 130 · Answer 3 · 2026-04-10 21:22:06

130

Views

How to prove a limit exists for $f(x)=(x+1)^2$ using the ϵ -δ definition of a limit

Published on 10 Apr 2026 - 21:22

score 186 · Answer 4 · 2026-04-15 05:26:07

186

Views

For all positive integers $a, b$, if $a$ is composite and $a$ divides $b$, then $b$ is composite.

Published on 15 Apr 2026 - 5:26

score 341 · Answer 5 · 2026-05-11 01:53:17

341

Views

Prove that we can divide a group of 90 people into 3 groups each with 30 people so that everyone has a friend in group

Published on 11 May 2026 - 1:53

score 700 · Answer 6 · 2026-04-16 10:28:19

700

Views

Showing $e(a,b)=\{\min(1,d(a,b))\}$ is equivalent to $d(a,b)$

Published on 16 Apr 2026 - 10:28

score 260 · Answer 7 · 2026-04-16 00:46:16

260

Views

Proving $3x^{10} - y^{10} = 1991$ has no integral solutions. Check my proof.

Published on 16 Apr 2026 - 0:46

score 339 · Answer 8 · 2026-04-12 23:03:01

339

Views

Norm of Fourier Sum operator $S_n$ on $\mathcal{L}^1$

Published on 12 Apr 2026 - 23:03

score 480 · Answer 9 · 2026-05-10 16:13:31

480

Views

Verify my proof for "For every $n, q$, where $n,q \in Z^+, n\geq 2, \sum_{i=1}^n\frac1n\neq q$". [$n^{th}$ harmonic number is never an integer]

Published on 10 May 2026 - 16:13

score 4.1k · Answer 10 · 2026-04-14 22:45:06

4.1k

Views

Prove B is a proper subset of A

Published on 14 Apr 2026 - 22:45

score 428 · Answer 11 · 2026-04-17 06:12:30

428

Views

Prove $(a,mn)=1\Rightarrow a^{{\rm lcm}(\phi(m), \phi(n))} \equiv 1 \pmod{\!mn} $

Published on 17 Apr 2026 - 6:12

score 2.3k · Answer 12 · 2026-04-13 20:03:57

2.3k

Views

Existence of a vector $v$ in $V$ such that the $T$-annihilator of $v$ is the minimal polynomial for $T$.

Published on 13 Apr 2026 - 20:03

score 2.3k · Answer 13 · 2026-04-20 13:01:32

2.3k

Views

Set of $n$ vectors spanning an $n$ - dim vector space implies set is a basis

Published on 20 Apr 2026 - 13:01

score 962 · Answer 14 · 2026-05-10 15:45:14

962

Views

Please check the proof of Imbedding theorem.

Published on 10 May 2026 - 15:45

score 76 · Answer 15 · 2026-04-15 17:02:16

76

Views

Show that $P(x,y)=0$ is a hyperbola if $b^2−4ac>0$ .

Published on 15 Apr 2026 - 17:02

List Question

If $\frac{x^2}{4}$ is an integer greater than 50, then what is the smallest possible value of $x^2$

How to solve this radical expression: $\frac 1{xy} \times (\sqrt{xy} - \frac{xy}{x-\sqrt{xy}})\times (\sqrt{xy} + \frac{xy}{x+\sqrt{xy}})$

How to prove a limit exists for $f(x)=(x+1)^2$ using the ϵ -δ definition of a limit

For all positive integers $a, b$, if $a$ is composite and $a$ divides $b$, then $b$ is composite.

Prove that we can divide a group of 90 people into 3 groups each with 30 people so that everyone has a friend in group

Showing $e(a,b)=\{\min(1,d(a,b))\}$ is equivalent to $d(a,b)$

Proving $3x^{10} - y^{10} = 1991$ has no integral solutions. Check my proof.

Norm of Fourier Sum operator $S_n$ on $\mathcal{L}^1$

Verify my proof for "For every $n, q$, where $n,q \in Z^+, n\geq 2, \sum_{i=1}^n\frac1n\neq q$". [$n^{th}$ harmonic number is never an integer]

Prove B is a proper subset of A

Prove $(a,mn)=1\Rightarrow a^{{\rm lcm}(\phi(m), \phi(n))} \equiv 1 \pmod{\!mn} $

Existence of a vector $v$ in $V$ such that the $T$-annihilator of $v$ is the minimal polynomial for $T$.

Set of $n$ vectors spanning an $n$ - dim vector space implies set is a basis

Please check the proof of Imbedding theorem.

Show that $P(x,y)=0$ is a hyperbola if $b^2−4ac>0$ .

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