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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Is this proof of 7 > 6 correct?

High-schooler here. I tried to prove that 7 > 6 because it's fun: Try Definitions 1D — $[a ≥ b] ↔ [a-(z) = b, z \in \mathbb{N}]$ 2D — $[a ≥ b] ↔ [(a=b) \lor (a>b)]$ 3D — $[a \neq b] ↔ ¬[a=b]$ Proof Using the identity axiom ($a + 0 = a$), we know…
user784856
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How to prove this statement. "There are not odd integers $x,y,z$ according to $(x-z)^2+(y-z)^2=(x+y)^2$."

I did try to prove this by contradiction(I guess it works). So I suppose this statement is false but I have confused about the meaning of it. If this statement is false it means "There are odd integers $x,y,z$ according to…
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Proof verification: $\sqrt{5}$ is the best possible value for Hurwitz's Theorem in Diophantine approximation

Hurwitz's Theorem: Let $\zeta$ be an irrational number, then there exist infinitely many coprime integers $p$ and $q$ such that $$\lvert \zeta - \frac{p}{q} \rvert < \frac{1}{\sqrt{5} q^2}$$ What I want to show is that if we substitute the $\sqrt5$…
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Show not possible to find positive whole numbers $m,n$ such that $m^2 − n^2 = 6$.

Show not possible to find positive whole numbers $m,n$ such that $m^2 − n^2 = 6$. $m^2 − n^2 = 6\implies (m+n)(m-n) = 6; \ m,n$ can be either even or odd. If $m$ is odd, $m=2k+1, k\ge 1$; else $m=2k$. Similarly, if $n$ is odd, $n=2l+1, l\ge 1$;…
jiten
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How fast is the village clock.

A man started from home at 14:30 hours and drove to a village, arriving there when the village clock indicated 15:15 hours. After staying 25 minutes, he drove back by a different route of length (5/4) times the first route at a rate twice as fast,…
Singh
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Maximizing $(\frac{N}{k})^k$ for integer k - proof

For a given integer $N$, we want to maximize $(\frac{N}{k})^k$. The solution in real numbers is obtained when $k = \frac{N}{e}$. The solution in integers is then either $\lfloor\frac{N}{e}\rfloor$ or $\lceil\frac{N}{e}\rceil$. However, it seems that…
kenor
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solving for $x^{\ln{(x)}}=1$

I think that I solved this equation, but there is still some dillema didi I did it right. Can you please check my solution, and see did I make any mistakes, and maybe propose another solution. $$ x^{\ln{(x)}}=1\\ \ln(x^{\ln{(x)}})=\ln(1)\\ \text{I…
depecheSoul
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Solution verification: solving $\sqrt{x-4}-\sqrt{x-5}+1=0$

I solved the following equation, and I just want to be sure I did it right. This is the procedure: $$ \sqrt{x-4}-\sqrt{x-5}+1=0\\ \sqrt{x-4}=\sqrt{x-5}-1\\ \text{squaring both sides gives…
depecheSoul
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Pairwise distinct $a ^ 3 b + b ^ 3 c + c ^ 3 a = a b ^ 3 + b c ^ 3 + c a ^ 3$ means they can't all have the same sign

Question Show that if $a, b, c$ are pairwise distinct real numbers and $$a ^ 3 b + b ^ 3 c + c ^ 3 a = a b ^ 3 + b c ^ 3 + c a ^ 3$$ then at least one of them is positive and at least one of them is negative. My idea First of all I put all the…
IONELA BUCIU
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Proof Verification: $2|n^2-n,\ \forall n\ \in \mathbb Z$

$$\text{Prove: } 2|n^2-n,\ \forall \ n \in \mathbb Z$$ My Proof is as follows. I am unsure as to how good it is and I presume there is a much better way of proving this that is simpler and clearer. Proof: $2|n^2-n,\ \forall \ n \in \mathbb Z$ there…
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Does this method to simplify certain equations always work?

In this question Peta asks if there is a simple method to solve for x in $$\dfrac{3+x}{2022}+\dfrac{2+x}{2023}+\dfrac{1+x}{2024}+\dfrac{x}{2025}=-4$$ There are some good replies in the comments of that question, but I was inspired to see if we can…
KDP
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Proof check of non existence of solutions in the Natural Numbers to $\frac{a^{2}+b^{2}}{a^{2}-b^{2}}$ + little doubt in the last line

I am currently practicing my proof writing skills and found a problem that asked to prove that there are not solutions in the natural numbers to :$\frac{a^{2}+b^{2}}{a^{2}-b^{2}}$ ($a$ and $b$ are natural numbers and $a>b$) I proceeded in the…
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Is my proof that $\sqrt{p}$ is irrational ($p$ is a prime) valid?

I'm learning mathematical proofs, and here I'm trying to prove that $\sqrt{p}$ is irrational, where $p$ is a prime number. Usually, the statement is proven by contradiction, assuming $\sqrt{p}$ is rational and there exist $m,n \in N$ without common…
g00dds
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Prove that for some $k$, there are polynomials $f_1(x),f_2(x),\ldots,f_k(x)$ such that $p(x)=\sum_{j=1}^k(f_j(x))^2$

Let $p(x)$ be a polynomial that is nonnegative for all $x\in\mathbb R$. Prove that for some $k$, there are polynomials $f_1(x),f_2(x),\ldots,f_k(x)$ such that $$p(x)=\sum_{j=1}^kf_j(x)^2$$ WLOG, assume the polynomial is monic. Now we can write…
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Function $f$ satisfying $f(x,y) = g(ax + by)$ and is continuous everywhere but not differentiable everywhere?

I am looking for a function $f : \mathbb{R_{0}^2} \to \mathbb{R_0}$ (where $\mathbb{R}_0$ is the set of non-negative reals) such that $f(x,y) = g(ax + by)$ for some $a,b > 0$ and $g : \mathbb{R_0} \to \mathbb{R}_0$, $f$ is continuous everywhere but…
supremacy
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