List questions from divisibility

Published on 28 Aug 2018 - 16:41

160

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Number theory: Divisibility in block of any size

Published on 28 Aug 2018 - 17:01

384

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$n^2 (n^4 - 1)$ is divisible by 60

Published on 29 Aug 2018 - 13:29

203

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Divisibility (Modular Arithmetics)

Published on 30 Aug 2018 - 15:07

293

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Can I show that a positive power of $2$ plus a perfect square is not divisible by $7$?

Published on 01 Sep 2018 - 4:08

38

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$3a4b \equiv 0\pmod{3}$, $3a4b \equiv 3\pmod{5}$

Published on 01 Sep 2018 - 13:09

403

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Tough Divisibility Problem

Published on 01 Sep 2018 - 15:31

48

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The four digit number $AABB$ can be divided by $6$ without remainder. Determine the greatest and least value of $AABB$.

Published on 02 Sep 2018 - 7:32

121

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Proof of $x$ is divisible by $11$, if $x^2$ is divisible by $11$

Published on 05 Sep 2018 - 14:27

131

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How to prove that for all natural $n$, $133|11^{n+2}+12^{2n+1}$

Published on 05 Sep 2018 - 18:20

36

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Number Theory: Divisibilty

Published on 22 Mar 2026 - 12:19

58

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Proving divisibility with modulo

Published on 07 Sep 2018 - 14:43

324

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$n^2 - n + 11$ is the product of four prime numbers, some of which may be the same. What is the minimum value of $n$?

Published on 07 Sep 2018 - 18:54

38

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Similar to Lehmar's totient problem

Published on 25 Mar 2026 - 18:47

249

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Prove that $6n+n^7$ is divisible by $7$ for $n>0$

Published on 09 Sep 2018 - 10:19

List Question

Number Theory: Divisibility on a set of consecutive integers

Number theory: Divisibility in block of any size

$n^2 (n^4 - 1)$ is divisible by 60

Divisibility (Modular Arithmetics)

Can I show that a positive power of $2$ plus a perfect square is not divisible by $7$?

$3a4b \equiv 0\pmod{3}$, $3a4b \equiv 3\pmod{5}$

Tough Divisibility Problem

The four digit number $AABB$ can be divided by $6$ without remainder. Determine the greatest and least value of $AABB$.

Proof of $x$ is divisible by $11$, if $x^2$ is divisible by $11$

How to prove that for all natural $n$, $133|11^{n+2}+12^{2n+1}$

Number Theory: Divisibilty

Proving divisibility with modulo

$n^2 - n + 11$ is the product of four prime numbers, some of which may be the same. What is the minimum value of $n$?

Similar to Lehmar's totient problem

Prove that $6n+n^7$ is divisible by $7$ for $n>0$

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