Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

15776 questions
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If $a:b:c=d:e:f$, how to show that $\frac{(a+b+c)^2}{(d+e+f)^2}=\frac{(ab+bc+ca)}{(de+ef+df)}$?

If $a:b:c=d:e:f$, how to show that $\frac{(a+b+c)^2}{(d+e+f)^2}=\frac{(ab+bc+ca)}{(de+ef+df)}$?
AYA
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Prove for all positive integers n that $7^{4n} −1$ is a multiple of $15$. You may not use proof by induction.

I factored this out to be $(7^n-1)(7^n+1)(7^{2n}+1)$, and I know I need to prove that I can always factor out a 3 and a 5, but I have no idea how to get there, especially without induction. My professor said I can use the rule of three consecutive…
Michael Johnston
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2 answers

Proving divisibility of integers

Given integers $x$ and $y$ and a prime number $k>3$. It turned out that $x + y$ and $x^2 + y^2$ are simultaneously divisible by $k$. Prove that $x^2 + y^2$ is divisible by $k^2$?
Anatoly Karpov
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Can someone help me with proof by contradiction?

How does one prove by contradiction that the sum of the squares of two odd integers cannot be the square of an even integer?
Murph Jones
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5 answers

Showing $|a+b|=|a|+|b|\iff ab\ge0$

I already proved the backward implication, and I was hoping I could get a hint for the forward. Would it be a proof by contradiction? The first part of the exercise was to prove the triangle inequality; would this be helpful here? I am not looking…
Alex D
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2 answers

let $m,n$ be two positive integers. prove that if $4$ does not divide $mn$, then $2$ does not divide $m$ or $2$ does not divide $n$

I understand there are two positive integers. I don't know how to prove that if $4$ does not divide $n$, then $2$ does not divide $m$ or $2$ does not divide $n$.
Rahul Godaba
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3 answers

Proof of composite

Prove that $\forall x \in \mathbb{N}, x^2 + 5x + 4$ is composite.
HKT
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3 answers

Are circular proofs valid

Suppose you want to prove statement A. To do this, you assume another statement, B, to be true. Using statement B, you prove A. Then using A, you prove B. Would this be a valid way of proving A? If not, what are some counter-examples?
Brian010515
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Prove that for all nonnegative real numbers $x, \frac {2|x-3|}{x+1} \le 7$

The question also says to consider two cases, based on the definition of absolute value. I am not sure how to prove this problem.
Deryn21
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How to show "if and only if"?

How to show "if and only if"? For example: Show that $x(t) \ge 0$ if and only if $x_e(t) \ge |x_o(t)|$ for all values of $t$, where $x_e(t)$ is the even part of $x(t)$ and $x_o(t)$ is the odd part of $x(t)$. Is it enough to show that the first…
JobHunter69
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Pick any three digit number

A Link to it is here: http://qr.ae/Rgrdrk In short, you take a 3 digit number, subtract the sum of it's digits. Any given digit in the result is equal to the difference between the other two numbers made into a 2-digit number and the next largest…
Jenjo
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Prove that if $n^6$ is a perfect square, $n^{50}$ is a perfect square.

Can someone help me prove/disprove this? I wrote $n^6$ as $l^2$, but I don't know how to convert $n^{50}$ into that format because $^{50}$ is too large. $n$ ∈ ℤ
user272513
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Extending the transitive property

Suppose we have a transitive relation $R$ on a set $S$. Suppose for some $n\in\mathbb{Z}^+\colon (s_0, s_1),(s_1,s_2),\ldots,(s_{n-1}, s_n)\in R$. Show that: $(s_0, s_n) \in R$ So I am having difficulties with everything past the basis case of…
GoingOnAHunt
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3 answers

Prove that $(x_1+x_2)^2 \neq x_1^2+x_2^2$

For $x_1, x_2 \in \mathbb{R}$ there is the rule: $(x_1\times x_2)^2=x_1^2\times x_2^2$. How can I prove, that this rule doesn't apply for: $(x_1+x_2)^2$?
Arthur
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2 answers

Determining whether an argument is valid or not

I am trying to determine whether an argument is valid. The question reads: "If $x^2 \neq 0$, where $x$ is a real number, then $x \neq 0$. Let $a$ be a real number with $a^2 \neq 0$; then $a \neq 0$". First of all I am confused by the two statements…
ComputerLocus
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