# Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. This should not be the only tag for a question.

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### $n!$ divides the product of $n$ consecutive integers if and only if $\binom{n}{k}\in\mathbb{N}$

For all $n\in\mathbb{N}$, $n!$ divides the product of $n$ consecutive integers if and only if for all $n,k\in\mathbb{N}$ if $0\leq k\leq n$ then $\binom{n}{k}\in\mathbb{N}.$ Firstly, I want to know ...
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### Is this method correct for this transportation problem?

I've attatched a picture of the question I am working on currently, note that this is a past exam paper with no mark scheme. I am only interested in solving part c, can anyone verify that this method ...
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### Validation: creating sequences given certain subsequences (one going to infinity and zero simultaneously)

I have problem with few exercises. I want to find a sequence that can create sequence that has different terms and has three subsequences: one going to minus inifnity, one to inifnity and other to ...
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### Find a pair of linear transformations that do not commute

The problem statement is as follows: Suppose $\mathbb{F}$ is any field. Find a pair of linear transformations $S,T \in \mathcal{L}(\mathbb{F^{2}}, \mathbb{F^2})$ such that $ST \neq TS$ My attempt ...
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### Spivak's Calculus, Ch. 11, **69b: $f$ increasing at every $a \in [0,1]$. Prove $f$ increasing on $[0,1]$.

A function $f$ is increasing at $a$ if there is some number $\delta>0$ such that $$f(x)>f(a) \text{ if } a<x<a+\delta$$ and $$f(x)<f(a) \text{ if } a-\delta<x<a$$ (a) Suppose ...
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### Proving that the following equation does not have integer solutions

I want to prove that the following equation has no integer solutions $a,b,c$: $$-a^3 - b^3 - c^3 + ab^2 - ac^2 + bc^2 - 2a^2c + 3abc = 0$$ apart from the naive solution $a=b=c=0$. The context, in case ...
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### Proof: How many continuous/bounded functions on $[0,1]$ verify $f(x)=f(x/2)\frac{1}{\sqrt{2}}$?

Question: How many continuous/bounded functions on $[0,1]$ verify $f(x)=f(x/2)\frac{1}{\sqrt{2}}$? Answer: Thank to @TonyK @Ryszard Szwarc. I think that i found an ever stronger demonstration that ...
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### Criterion for uniform continuity multivariable calculus

Let $D\subset \Bbb{R}^n$ be an open set (non empty) and convex. Let $f:D\to \Bbb{R}$ be a $C^1(D)$ function s.t $\exists C \in \Bbb{R}$ s.t $\|\nabla f(x)\|\leq C \ \forall x \in D$. Show that $f$ is ...
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