List questions from elementary-number-theory

Published on 12 Apr 2026 - 3:27

95

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When is $2\cos(\pi \frac{i}{n}) + 2\cos(\pi \frac{j}{m}) = -1 $

Published on 16 Apr 2026 - 14:49

523

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A non-composite sequences

Published on 14 Apr 2026 - 15:06

326

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If an integer n, greater

Published on 13 Apr 2026 - 21:16

106

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Incorrect proof of Wilson's Theorem?

Published on 13 Apr 2026 - 10:26

131

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Can the smallest solution of $\varphi(k)=n$ be an even positive integer?

Published on 17 May 2026 - 3:55

63

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Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

Published on 14 Apr 2026 - 21:31

100

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If $a,b,c,d\in\mathbb{Z^+}$ where $ad=b^2+bc+c^2$, prove that $a^2+b^2+c^2+d^2$ is composite

Published on 16 Apr 2026 - 10:35

35

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Checking Proof for the following Divisibility

Published on 16 Apr 2026 - 17:05

139

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Showing that $p$ is an odd prime $\iff$ $\forall a \in \Bbb N$ $gcd(a,p)=1$ or $gcd(a,p)=p$

Published on 15 Apr 2026 - 23:05

246

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How to count all the solutions for $\sum\limits_{i=1}^{n} \frac{1}{2^{k_i}}= 1$ for $k_i\in \Bbb{N}$ and $n$ a fixed positive integer?

Published on 11 May 2026 - 3:17

188

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If $n$ is even, which values could $n \% 4$ be equal to?

Published on 17 Apr 2026 - 2:19

713

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Understanding fractions in modular arithmetic

Published on 08 Apr 2026 - 5:20

166

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Prove that there are no positive integer solutions for $a,b,c,d$ if $a^2-b=c^2, b^2-a=d^2$

Published on 13 Apr 2026 - 18:18

314

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Generating Function For Catalan Numbers Type Sequence

Published on 11 May 2026 - 15:33

List Question

Is there a sequence of natural numbers with these properties?

When is $2\cos(\pi \frac{i}{n}) + 2\cos(\pi \frac{j}{m}) = -1 $

A non-composite sequences

If an integer n, greater

Incorrect proof of Wilson's Theorem?

Can the smallest solution of $\varphi(k)=n$ be an even positive integer?

Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

If $a,b,c,d\in\mathbb{Z^+}$ where $ad=b^2+bc+c^2$, prove that $a^2+b^2+c^2+d^2$ is composite

Checking Proof for the following Divisibility

Showing that $p$ is an odd prime $\iff$ $\forall a \in \Bbb N$ $gcd(a,p)=1$ or $gcd(a,p)=p$

How to count all the solutions for $\sum\limits_{i=1}^{n} \frac{1}{2^{k_i}}= 1$ for $k_i\in \Bbb{N}$ and $n$ a fixed positive integer?

If $n$ is even, which values could $n \% 4$ be equal to?

Understanding fractions in modular arithmetic

Prove that there are no positive integer solutions for $a,b,c,d$ if $a^2-b=c^2, b^2-a=d^2$

Generating Function For Catalan Numbers Type Sequence

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