List questions from divisibility

Published on 27 Sep 2019 - 14:20

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Calculate percentage of number between min and max

Published on 26 Mar 2026 - 13:51

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Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

Published on 27 Sep 2019 - 16:16

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What are the number of ordered pairs $(x,y)$ where both $x$ and $y$ divide $20^{19}$, however $xy$ doesn't?

Published on 28 Sep 2019 - 0:30

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Prove $(m!)^3(n!)^4|(3m)!(4n)!$ for all positive integers $m,n$

Published on 27 Mar 2026 - 10:10

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Explanation of Divisibility in Lucas' Theorem Proof

Published on 29 Sep 2019 - 4:56

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Why does the growth rate of integers $n$ for which $\varphi(x) = n$ has no solutions increase suddenly after a point?

Published on 26 Mar 2026 - 19:03

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Show divisibility $\,1998\mid 760^{1998} - 20^{1998} + 1910^{1998} - 652^{1998}$

Published on 29 Sep 2019 - 16:00

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A question on the Stirling numbers

Published on 26 Mar 2026 - 17:43

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Multiplicativity of the Divisor Function

Published on 30 Sep 2019 - 17:15

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How to proof the following property?

Published on 23 Feb 2026 - 4:53

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For every natural number $n$, prove that $4\mid(3^n-1)$ iff $4$ does not divide $3^n+1$

Published on 01 Oct 2019 - 9:03

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"Among any $n+1$ integers not exceeding $2n$, one of the integers divides the other" isn't true? $n=10$ for example?

Published on 28 Mar 2026 - 6:00

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Is $a \sim b$ such that $\gcd(a,b) > 1$ an equivalence relation?

Published on 29 Mar 2026 - 6:29

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Divisibility question: if $a=be+r$, then $e$ $= ⌊\frac{a}{b}⌋$

Published on 12 Mar 2014 - 1:14

List Question

Cousins to each other (divisibility)

Calculate percentage of number between min and max

Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

What are the number of ordered pairs $(x,y)$ where both $x$ and $y$ divide $20^{19}$, however $xy$ doesn't?

Prove $(m!)^3(n!)^4|(3m)!(4n)!$ for all positive integers $m,n$

Explanation of Divisibility in Lucas' Theorem Proof

Why does the growth rate of integers $n$ for which $\varphi(x) = n$ has no solutions increase suddenly after a point?

Show divisibility $\,1998\mid 760^{1998} - 20^{1998} + 1910^{1998} - 652^{1998}$

A question on the Stirling numbers

Multiplicativity of the Divisor Function

How to proof the following property?

For every natural number $n$, prove that $4\mid(3^n-1)$ iff $4$ does not divide $3^n+1$

"Among any $n+1$ integers not exceeding $2n$, one of the integers divides the other" isn't true? $n=10$ for example?

Is $a \sim b$ such that $\gcd(a,b) > 1$ an equivalence relation?

Divisibility question: if $a=be+r$, then $e$ $= ⌊\frac{a}{b}⌋$

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