Mathematics Stack Exchange
Mathematics Stack Exchange

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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Find locus of the points $(x,y)$ such that $x^3+y^3+3xy=1$

Find locus of the points $(x,y)$ such that $x^3+y^3+3xy=1$ $\textbf{My solution}:$ We notice that $(x+y)^3=x^3+y^3+3xy(x+y)$, putting $x+y=1$ gives us our desired equation. Hence all the points satisfying $x+y=1$ is gives us all the points…
Ellie_Wong
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How can I verify that I have all solutions of a system of equations with absolute values

The problem is proposed as follows: For two real numbers $a$ and $b$ with $|a| \neq |b| $ find all solutions to the following system of equations: $x + |y| = a$ and $|x| + y = b$, where $x$ and $y$ are real numbers. I approached this problem by…
Ams1901
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Exercises solutions for "Game Physics Development" by Ian Millington

Does anyone have the exercise solutions for Game Physics Development by Ian Millington? I can't seem to find them anywhere. Thank you in advance.
Ben Serrano
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How to prove that the gradient is a covariant tensor? (make it simple and clear)

I know that all vectors are contravariant because if we transform into another basis vector we find its components change inversely to its original components. But I don't know why gradient is a covariant. How the components changes same as basis…
professor T
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Showing that a function is an injection.

I am a applied mathematician and I want to return to study in a pure mathematical field. I am working through a textbook and I want some pointers with the following proof. Consider the following map: $$g: i \in \mathbb{Z} \mapsto 2i \text{ if } i >…
HMPtwo
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If for $a,b,x \in \mathbb{N}$ if we have $a \mid x, b \mid x$ prove that $\operatorname{lcm} (a,b) \leq x$

If for $a,b,x \in \mathbb{N}$ if we have $$a \mid x, b \mid x$$ prove that $\operatorname{lcm} (a,b) \leq x$ My solution: maximum value of $a,b$ is when they are both $x$, in which case their lcm is also $x$, but if any of them are less than $x$…
math_learner
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Every number n > 6 is sum of two numbers $a$ and $b$ with $a,b>1$ and $gcd(a,b)=1$

I was working on this question and came up with this answer: Take any prime number $p$ that’s greater than $\frac{n}{2}$. Let $a=p$ and $b=n-p$, then b is necessarily smaller than a because $p>\frac{n}{2}$ and $gcd(a,b)=1$, because $p$ is…
J3ck_Budl7y
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Contest Problem - HMMT 2

Compute the number of ways to tile a 3 × 5 rectangle with one 1 × 1 tile, one 1 × 2 tile, one 1 × 3 tile, one 1 × 4 tile, and one 1 × 5 tile. (The tiles can be rotated, and tilings that differ by rotation or reflection are considered…
Satish Ramanathan
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Contest Problem - HMMT

There are 800 marbles in a bag. Each marble is colored with one of 100 colors, and there are eight marbles of each color. Anna draws one marble at a time from the bag, without replacement, until she gets eight marbles of the same color, and then she…
Satish Ramanathan
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Is this proof of the irrationality of $\sqrt{3}$ using only the definition of an even number valid?

Suppose for the sake of contradiction that $\sqrt{3}$ is rational. Then $\sqrt{3} = p/q$ for $p,q \in \mathbb{Z}$. Also assume that $p$ and $q$ have no common divisor, thus $p$ and $q$ can't both be even. So, $\sqrt{3} = p/q \implies 3 = p^2/q^2…
lopan
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Is my proof of showing "4rs is even" correct?

For my study I need to write proofs. I have a hard time understanding that if my answer isn't the same as in the solution book, if it then can still be correct. The Question given is : "Prove that $4rs$ is even , with $r$ & $s$ Integers" Here's the…
Diceble
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I want to prove that some functions are not one-to-one. Are both notations correct?

I want to prove that some functions are not one-to-one. Are both these proofs written correct? $\exists\,x_1=1,\,x_2=-1\;[1\neq -1 \wedge f(1)=f(-1)]$ $\exists\,x_1=1,\,x_2=-1\;[x_1\neq x_2 \wedge f(x_1)=f(x_2)]$
DScounterGO
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Proof of absolute convergence and divergence of $ \zeta(s) $

Is this a valid proof of absolute convergence of $ \zeta(s) $ for $ \Re(s) > 1 $ and divergence of $ \zeta(s) $ for $ \Re(s) < 0 $? By integral test for convergence, $ \sum_{n=1}^{\infty} \left| \frac{1}{n^s} \right| $ converges if and only if $…
Lone Learner
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Using newton's method to evaluate the critical point of $f(x)=\sin x - \ln x$

If Newton's method to applied to find the critical point of the $f(x) = \sin x - \ln x$, i.e., a point where $f'(x) = 0$, which iteration formulas should be obtained? So basically I used the newton's method to approximate the root for $f'(x) = 0$,…
Y.T.
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Prove that $7 | (3^{2n} − 2^{n} )$ for every nonnegative integer $n$.

I tried to format my question but I couldn’t figure out how to do it. Prove that $7 | (3^{2n} − 2^{n})$ for every nonnegative integer $n$. my proof: Basic step (0): 7 | 1-1 which is true. Ind. step: if $p(k) \implies p(k+1)$: $3^{2k} −…
JackSymBol
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