List questions from divisibility

Published on 27 Aug 2016 - 6:52

234

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Is it true that if $n$ is a Carmichael number then $n-1$ cannot be square free?

Published on 27 Aug 2016 - 11:59

398

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A necessary and sufficient condition for Carmichael numbers

Published on 28 Aug 2016 - 9:24

421

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Two different numbers are divided by 7

Published on 29 Aug 2016 - 3:00

87

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Check if an expression is divisible by 2016. (modulo operations?)

Published on 29 Aug 2016 - 9:34

42

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Show that $13$ is the only prime such that $d(p(2p+1))=8$ and $2p+1$ is NOT semiprime where $d$ is the divisor counting function.

Published on 29 Aug 2016 - 16:16

3.4k

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Largest divisor of $P(n) = (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)$

Published on 30 Aug 2016 - 8:11

2.8k

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Prove that $4^n+ 1$ is not divisible by $3$

Published on 31 Aug 2016 - 18:16

649

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Finding the remainder of a factorial raised to more factorials when divided by 11

Published on 31 Mar 2026 - 2:20

257

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Divisibility of the pth Stirling number of the first kind (edit:of the second order)

Published on 27 Mar 2026 - 6:05

458

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When does a prime $p=m^2+n^2$ divide the term $ m^3+n^3-4$?

Published on 01 Sep 2016 - 18:48

161

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True or False: If $a$|$b^2$ then $a^2$|$b^4$.

Published on 01 Sep 2016 - 21:23

367

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${\rm gcd}(x,y)$ dividing linear combination of $x$, $y$

Published on 30 Mar 2026 - 0:20

43

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Equivalent conditions on $d$ being a common divisor of $a$ and $b$ in an integral domain: $(a,b) \subseteq (d) \Leftrightarrow d|a$ and $d|b$

Published on 26 Mar 2026 - 11:01

108

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Finding the maximum value of $abcdef$ given certain conditions of the divisibility of ab, abc, abcd, ...

Published on 02 Sep 2016 - 22:31

List Question

If $3\mid a$, then $3\mid a^2$

Is it true that if $n$ is a Carmichael number then $n-1$ cannot be square free?

A necessary and sufficient condition for Carmichael numbers

Two different numbers are divided by 7

Check if an expression is divisible by 2016. (modulo operations?)

Show that $13$ is the only prime such that $d(p(2p+1))=8$ and $2p+1$ is NOT semiprime where $d$ is the divisor counting function.

Largest divisor of $P(n) = (n + 1)(n + 3)(n + 5)(n + 7)(n + 9)$

Prove that $4^n+ 1$ is not divisible by $3$

Finding the remainder of a factorial raised to more factorials when divided by 11

Divisibility of the pth Stirling number of the first kind (edit:of the second order)

When does a prime $p=m^2+n^2$ divide the term $ m^3+n^3-4$?

True or False: If $a$|$b^2$ then $a^2$|$b^4$.

${\rm gcd}(x,y)$ dividing linear combination of $x$, $y$

Equivalent conditions on $d$ being a common divisor of $a$ and $b$ in an integral domain: $(a,b) \subseteq (d) \Leftrightarrow d|a$ and $d|b$

Finding the maximum value of $abcdef$ given certain conditions of the divisibility of ab, abc, abcd, ...

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