List questions from elementary-number-theory

Published on 10 Apr 2026 - 3:37

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Puzzle (1): Explaining a pattern in multiplication graphs modulo $m$

Published on 17 Apr 2026 - 0:35

119

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$n|a^n-b^n\Rightarrow n|\frac{a^n-b^n}{a-b}$

Published on 16 Apr 2026 - 18:41

160

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Prove $n{2n\choose n}=(n+1){2n\choose n-1}$ and $(n+1)|{2n\choose n}$

Published on 15 Apr 2026 - 4:35

70

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How to calculate divisibility with 3 of a ratio?

Published on 10 Apr 2026 - 7:36

473

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Divisibility represented by Boolean logic

Published on 10 May 2026 - 15:41

59

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If $p$ is a prime and $(a,b)=1$ then there is a $k \in \{ 0, \dots, p-1 \}$ s.t. $p | (a-kb)$?

Published on 15 Apr 2026 - 16:21

184

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Inverse Fermat's theorem

Published on 14 Apr 2026 - 10:52

258

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Is $10^{2^{21}}+1$ known to be composite?

Published on 14 Apr 2026 - 13:40

46

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Euclidean algorithm in Euclid's words

Published on 10 May 2026 - 20:00

493

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Factoring a large semi-prime number.

Published on 15 May 2026 - 1:23

1.3k

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If $n$ is composite then there are integers $a$ and $b$ such that $n$ divides $ab$ but $n$ divides neither $a$ nor $b$.

Published on 15 Apr 2026 - 20:12

305

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Finding the remainder of $823^{823}$ in the division by 11

Published on 13 Apr 2026 - 15:06

189

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Regarding square-free integers and Euler's function

Published on 13 Apr 2026 - 21:49

123

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Prove the sum from $1$ to $n$ is congruent to half $n$ or $0$ for even or odd values of $n$

Published on 17 Apr 2026 - 4:33

List Question

Proof Explanation - Odd prime division

Puzzle (1): Explaining a pattern in multiplication graphs modulo $m$

$n|a^n-b^n\Rightarrow n|\frac{a^n-b^n}{a-b}$

Prove $n{2n\choose n}=(n+1){2n\choose n-1}$ and $(n+1)|{2n\choose n}$

How to calculate divisibility with 3 of a ratio?

Divisibility represented by Boolean logic

If $p$ is a prime and $(a,b)=1$ then there is a $k \in \{ 0, \dots, p-1 \}$ s.t. $p | (a-kb)$?

Inverse Fermat's theorem

Is $10^{2^{21}}+1$ known to be composite?

Euclidean algorithm in Euclid's words

Factoring a large semi-prime number.

If $n$ is composite then there are integers $a$ and $b$ such that $n$ divides $ab$ but $n$ divides neither $a$ nor $b$.

Finding the remainder of $823^{823}$ in the division by 11

Regarding square-free integers and Euler's function

Prove the sum from $1$ to $n$ is congruent to half $n$ or $0$ for even or odd values of $n$

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