List questions from divisibility

Published on 24 Sep 2015 - 15:19

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Number Theory Positive Divisor Problems

Published on 12 Apr 2026 - 6:29

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Prove these two elements are not associated in $\mathbb Q[x,y,z]/(x-xyz)$

Published on 25 Sep 2015 - 3:03

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Prove that $2^n+(-1)^{n+1}$ is divisible by 3.

Published on 11 Apr 2026 - 17:04

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Number Theory Prime Reciprocals never an integer

Published on 13 Apr 2026 - 0:07

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divisibility question: if two integers can both divide each other, do they have to be equal?

Published on 13 Apr 2026 - 5:50

54

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Knapsack - Saving Waste

Published on 09 Apr 2026 - 0:57

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If $r$ is a nonzero solution $ x^2 + ax + b$, prove that $r | b$

Published on 26 Sep 2015 - 21:37

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Order of group element divides order of finite group

Published on 26 Sep 2015 - 21:54

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Divisibility test using perhaps binomial thorem

Published on 13 Apr 2026 - 3:56

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$\frac{2n\choose n}{n+2}\not\in\mathbb N$ and $n\neq3k+1$ and $n\neq4k+2$

Published on 28 Mar 2026 - 15:21

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Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$

Published on 03 Apr 2026 - 7:32

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Prove that if a|b, c|d, then ac|bd

Published on 27 Sep 2015 - 21:03

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Let N be a four digit number, and N' be N with its digits reversed. Prove that N-N' is divisble by 9. Prove that N+N' is divisble by 11.

Published on 28 Sep 2015 - 4:20

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Expected number of digits of the smallest prime factor of $1270000^{16384}+1$

Published on 13 Apr 2026 - 7:05

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Maximum amount of divisors of the number $n^m+m^n$

Number Theory Positive Divisor Problems

Prove these two elements are not associated in $\mathbb Q[x,y,z]/(x-xyz)$

Prove that $2^n+(-1)^{n+1}$ is divisible by 3.

Number Theory Prime Reciprocals never an integer

divisibility question: if two integers can both divide each other, do they have to be equal?

Knapsack - Saving Waste

If $r$ is a nonzero solution $ x^2 + ax + b$, prove that $r | b$

Order of group element divides order of finite group

Divisibility test using perhaps binomial thorem

$\frac{2n\choose n}{n+2}\not\in\mathbb N$ and $n\neq3k+1$ and $n\neq4k+2$

Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$

Prove that if a|b, c|d, then ac|bd

Let N be a four digit number, and N' be N with its digits reversed. Prove that N-N' is divisble by 9. Prove that N+N' is divisble by 11.

Expected number of digits of the smallest prime factor of $1270000^{16384}+1$

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