# Tagged Questions

For questions about approaches and techniques for discovering a proof, as opposed to writing it down clearly (which involves (proof-writing)). Should not be used unless the focus is on the technique of the proof instead of the solution.

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### Proof: Lemma 5.6.2 - Elements of Real Analysis (C.G. Denlinger)

I reading the book "Elements of Real Analysis, C.G.Denlinger".. and I need the proof of Lemma 5.6.2: Thanks in advance!
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### Can we prove that this tabular algorithm works correctly?

Finding an answer to the following question is very important, because it will help prove an algorithm works correctly. It is also extremely hard to explain, so I'm hoping that someone will help me ...
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### Discrete Mathematics Proof Question

Prove or disprove that there are infinitely many $x, y, z \in \mathbb N$ such that $$\frac{1}{x^2} + \frac{1}{y^2} = \frac{1}{z^2}$$ Currently, I tried to substitute $x, y,$ and $z$ with $2n$ and $n$ ...
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### Discrete mathematics proof relating to Fermat's Theorem

Assuming the Fermat Theorem, show that there is no natural number $x$, $y$, and $z$ and $n\geq3$ such that $$\frac{1}{x^n} + \frac{1}{y^n} = \frac{1}{z^n}.$$ So far I think proof by contradiction ...
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### Help with a proof in discrete math.

I have been trying to figure out this problems to no avail. Problem $1$: Show that there are infinitely many natural numbers $x,y,z$ such that $$\frac{1}{x} + \frac{1}{y} = \frac{1}{z}.$$ Thank ...
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### Prove or Disprove the existence of a basis

I'm asked to prove or disprove the existence of a basis $(p_0,p_1,p_2,p_3)$ of $F(t)(3)$ (Polynomials of degree at most 3) such that each of the polynomials $p_0,p_1,p_2,p_3$ satisfies the equation ...
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### Suppose $G=\{a_1,\dots a_n\}$ is a finite abelian group and $a^2\neq e$ for all nonidentity elements. What is the product $a_1a_2\dots a_n$?

Let $G$ be a finite abelian group such that for all $a \in G$, $a\ne e$, we have $a^2\ne e$. If $a_1, a_2, \ldots, a_n$ are all the elements of $G$ with no repetitions, what is the product \$a_1 a_2 ...