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Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

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Functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $f \big(x ^ 2 + y ^ 2f (x)\big) = xf (y) ^ 2-f (x) ^ 2$

Find all functions $ f : \mathbb R \to \mathbb R $ satisfying $$ f \left ( x ^ 2 + y ^ 2 f ( x ) \right ) = x f ( y ) ^ 2 - f ( x ) ^ 2 $$ for all $ x , y \in \mathbb R $. Let $P(x,y)$ denote the functional equation. $P(0,0)$ gives $f(0)=-f(0)^2…
Lambert macuse
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Traffic equation to get loop sensor occupancy from traffic density

I am curious about the justification and validity of a traffic equation we are currently about to use within our research- and working group. It is about the relationship between an inductive loop sensors $s$ occupancy duration $OCC_s$, the traffic…
marc wellman
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Why does $\lambda (e^x - 1) = x$ have two solutions for $\lambda > 1$?

Apparently $\lambda (e^x - 1) = x$ has two solutions for $\lambda > 1$. My textbook is kind of handwaving and saying that this is true without explaining. Can somebody prove this for me or show me why this is true? I understand why $x=0$ is always a…
Steady
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Can someone just check this for me please

I have an exam and this has stumped me. I think it is a typo error. So this is part of the question. a curve of the form $y = Ax^3$, where A is a constant, joining the two endpoints $(1,1)$ and $(2,4)$. The answer that has been given is…
user118282
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How do you prove that a function is independent of a variable in an interval?

I was doing basic excercises about proofs but I am lost with this one. "Prove taht if a is a fixed value in the interval {$0
Javier Lázaro
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$p$-adic integers form integral doamain

I am trying to prove that the ring of $p$-adic integers contains no zero-divisors. Let $(a_n)$ and $(b_n)$ be $p$-adic integers (so $a_i\in\mathbb{Z}/p^i$ and $a_{n+1}\equiv a_n \pmod{p^n}$ and same for $b$'s). If these numbers are non-zero, let…
Maths Rahul
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Trying to formally understand the proof of $m,n\in \Bbb{N}$ with $m>n$ then $m-n\in \Bbb{N}$?

I'm trying to understand the meaning of the solution of the following problem: Formally, what are we actually proving here? When I prove things by induction, I try to write the predicate I'm trying to prove. In this case, I guess the predicate…
Red Banana
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Construct an equation of the parabola $y^2=2px$ in polar coordinates, where it's vertex is at $(0,0)$.

I got $\begin{split} &r^{2}\sin^{2}\varphi=2pr\cos\varphi \\& r(r\sin^{2}\varphi-2p\cos\varphi)=0 \\& r\sin^{2}\varphi-2p\cos\varphi=0 \implies r=\frac{2p\cos\varphi}{\sin^{2}\varphi} \end{split}$ So I got…
hellusENG
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Need a bit of clarification of what the question is asking?

Suppose a and b are positive integers. Consider the following statement P: If 4 ∤ a and 4 ∤ b then 4 ∤ ab. Write down the converse and contrapositive of P. Which of the three statements — P itself, the converse of P, and the contrapositive of P —…
HasBeen22
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Prove that a function with bounded derivative is bounded

Let a $f$ be a function on $[a,b]$ such that it's differentiable on $(a,b)$ such that $|f'(x)| \leq M$ for some real $M$. Prove that $f$ is also bounded. My proof: Fix an arbitrary $x_0 \in (a,b)$ then for all $k \in (a,x_0)$, then by MVT, there…
zaemon_23
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Show that if a and d are positive integers, then (−a) div d = −a div d if and only if d divides a.

Let $a$ and $d$ be positive integers. We assume $(-a)/d=-a/d$. By definition, $a=dq+r$, where $q$ and $r$ are arbitrary integers such that $0\leq r
Gabriel Dylan
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Show that the difference between consecutive perfect squares is odd.

Let both $x$ and $y$ be arbitrary naturals and perfect squares. By definition, a perfect square can be written in the form $k^2$, for some natural $k$. So we can write $x = (k+1)^2$ and $y=k^2$, where $k$ is an arbitrary natural. Thus,…
Gabriel Dylan
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Constructing $\sqrt{n}$ as the length of a right triangle

I'm reading Martin Liebek's book, and he gives a construction of $\sqrt{n}$ as the side length of a triangle, but leaves the verification as an exercise. It's a bit difficult to describe the picture in full without drawing it, but the construction…
Brad G.
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Proving that if $x$ is irrational, then $\frac1x$ is irrational

I was given the question: Prove that if $x$ is irrational, then $\frac1x$ is irrational I did this through contraposition, namely: if $\frac1x$ is rational, it can be written in the form $\frac ab$ where b is nonzero. Thus, $\frac1x = \frac ab$…
Willem
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For a function $f:[a,b]\rightarrow \mathbb(R)$, prove that there exists a $x_0$ so that $f^{(n)}(x_0)=0, x_0 \in [a,b]$

Let $n\in\mathbb{N}$. The function $f:[a,b]\rightarrow \mathbb{R}$ is n-times differentiable. Let $x_1,...,x_{n+1} \in [a,b]$ with $x_1<...
J3ck_Budl7y
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