# Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

2,586 questions with no upvoted or accepted answers
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### Is there a group theoretic proof that $(\mathbf Z/(p))^\times$ is cyclic?

Theorem: The group $(\mathbf Z/(p))^\times$ is cyclic for any prime $p$. Most proofs make use of the fact that for $r\geq 1$, there are at most $r$ solutions to the equation $x^r=1$ in $\mathbf Z/(p)$...
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### Trying to prove a proposition about the nth order derivative of a polynomial by induction - is this correct?

Recently, I decided to try and create a formula for the $n$th order derivative of a polynomial, and I believe I succeeded! I tried to do a proof by induction to confirm this for myself, but since I ...
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### Is there a Sokoban level with such conditions

First of all, let me explain what Sokoban is. It is a logic game created in Japan and it literally means "warehouse keeper". It is a type of transport puzzle, in which the player pushes boxes or ...
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### Cauchy-Formula for Repeated Lebesgue-Integration

Recently, I came across the following statements. They were annotated as consequences of Fubini's Theorem but neither proof nor reference were given. Let $f:[a,b]\times [a,b]\to\mathbb{R}$ be ...
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### Controlled natural language for mathematics

I am a French student very inspired by Bourbaki's but I can no longer stand to write approximate proofs. I was wondering if there was a language between formal and natural language that was both non-...
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### Olympic number theory problem: is this solution fine and sufficiently well written?

Determine all positive integers $m$ such that the ratios $$\frac{2(5^m+5)}{3^m+1}\quad\text{and}\quad \frac{9^m+1}{5^m+5}$$ are both integers. Attempt at a solution: If the ratios are both ...
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### About Theorem 3.4 Hartshorne: detailed proof.

I propose a detailed version of part of the proof of Theorem 3.14 from Hartshorne's book Algebraic Geometry. The questions are inserted from time to time within the proof. Thanks for your patience. ...
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### Degree of hypersurfaces in Grassmannians

In the book Discriminants, Resultants, and Multidimensional Determinants of Andrei Zelevinsky and Izrail' Moiseevič Gel'fand, the authors give the following definition of degree of a hypersurface in a ...
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### Can a product of a number and its reverse consist of only $1$'s?

Problem: Let $n \gt 1$. If you write the digits of $n$ in reverse, then multiply by original $n$, is it possible for the product to consist only of $1$'s? This came from a competition I recently ...
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### Differential geometry: non-uniqueness of the closest point on a curve

I have looked for theorems about the closest points, but I could not find such a theorem I need to establish some other claim. The main question is expressed as a proposition as follows: Proposition: ...
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### Proof Strategy for a Dynamical System of Points on the Plane

I have a rather simple-looking system which exhibits a particular behaviour in simulation, and I would now like to attempt to prove this formally. The problem is, I don't really know where to start, ...
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### Improving clarity and argumentation with hard-to-describe combinatorial proof

I'm doing undergraduate research and the content of my paper depends on the following lemma. I tried something like a combinatorial proof, but it is clearly not rigorous, partly because my argument is ...
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### Prove that $||x+y|| \leq ||x|| +||y||$

From Munkres' Topology, I get this question. A hint suggests us to use a result from a previous subquestion. But it seems that I don't need to use the previous result to prove this. Can someone help ...
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### Have there been any (interesting) computer-aided proofs that weren't proof-by-exhaustion?

It seems to me like many of the most famous "computer proofs" were done by basically brute-forcing through all of the cases, such as the four color map theorem. Are there any good examples of computer ...
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### complex number to a power divisible by 6

I actually have a follow-up question to this post -- given that n is a positive integer such that $z^n = (z+1)^n = 1$, I need to show that n is divisible by 6. I can now show that $z$ and $z+1$ both ...
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### How do you prove this implication using its contrapositive?

$∀x∈R,|2x-1|≤5$ and $|2x-1|>3⇒(x^4+7≤7x^2 )$ or $(2x^3≥8x+5)$ This is what I got for the contrapositive: $∀x∈R,(x^4+7>7x^2 )$ and $(2x^3<8x+5)⇒|2x-1|>5$ or $|2x-1|≤3$ Where would I ...
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### How to make a proof your own?

Often, in the interest of time, We look at proofs done by others. It could be on stack, in a textbook, or shown by a friend. In all cases, you don't get the same amount of mental compression of the ...
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