List questions from proof-explanation

Published on 21 Apr 2026 - 13:49

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Olympiad Functional Equation $f(xf(y))=yf(x)$

Published on 13 Apr 2026 - 16:34

105

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Why $\sum_{k=m}^n\binom{n}{k}\binom{k}{m} = \binom{n}{m}2^{n-m},0< m< n$?

Published on 16 Apr 2026 - 19:28

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Step in proof of Goldstine Theorem

Published on 25 Mar 2026 - 19:10

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Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$

Published on 14 Apr 2026 - 9:28

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Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $

Published on 16 Apr 2026 - 10:09

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Let $ϕ: R → S$ be a ring homomorphism, where $S$ is a domain. Prove that if $u ∈ R$ is nilpotent then $u ∈ \ker ϕ$.

Published on 14 Apr 2026 - 22:06

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How to prove that Cantor ternary set has no intervals using ternary expansions?

Published on 12 Apr 2026 - 5:57

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How to prove $x^2 + y^2 + z^2\geq xy + xz + yz$

Published on 15 Apr 2026 - 17:49

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Examples of $(x,y)\in\mathbb{R}^2$ with different distances for every $P\in\mathbb{R}^2$

Published on 14 Apr 2026 - 5:14

81

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Why is the limit of a argument for closedness of the unitary group correct?

Published on 25 Mar 2026 - 11:16

65

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Understanding the proof of the existence of a clopen set in an exercise.

Published on 09 Apr 2026 - 10:07

154

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Showing that $A_q(n,1)=q^n$ in the Main Coding Theory Problem.

Published on 15 Apr 2026 - 11:19

166

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Limit of $\frac{f(1+h)-f(1-3h)}{5h}$

Published on 13 Apr 2026 - 20:26

136

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On Littlewood Conjecture

Published on 15 Apr 2026 - 1:13

List Question

In $Q_p$: $f(x)=0$ iff $p(f(x))^2$ is a square

Olympiad Functional Equation $f(xf(y))=yf(x)$

Why $\sum_{k=m}^n\binom{n}{k}\binom{k}{m} = \binom{n}{m}2^{n-m},0< m< n$?

Step in proof of Goldstine Theorem

Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$

Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $

Let $ϕ: R → S$ be a ring homomorphism, where $S$ is a domain. Prove that if $u ∈ R$ is nilpotent then $u ∈ \ker ϕ$.

How to prove that Cantor ternary set has no intervals using ternary expansions?

How to prove $x^2 + y^2 + z^2\geq xy + xz + yz$

Examples of $(x,y)\in\mathbb{R}^2$ with different distances for every $P\in\mathbb{R}^2$

Why is the limit of a argument for closedness of the unitary group correct?

Understanding the proof of the existence of a clopen set in an exercise.

Showing that $A_q(n,1)=q^n$ in the Main Coding Theory Problem.

Limit of $\frac{f(1+h)-f(1-3h)}{5h}$

On Littlewood Conjecture

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