List questions from divisibility

Published on 16 Nov 2018 - 14:04

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proof that the sum of digits of natural number are divisible by 3 iff the number is

Published on 18 Nov 2018 - 17:44

86

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$2^{b}-1$ does not divide $2^{a}+1$

Published on 18 Nov 2018 - 17:48

873

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Infinite sequence $2^{n}-3 (n=2,3,...)$ contains no term divisible by 65

Published on 18 Nov 2018 - 18:47

101

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Checking if the Product of n Integers is Divisible by Prime N

Published on 26 Mar 2026 - 1:34

102

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How to prove an equivalence of two equations?

Published on 26 Mar 2026 - 11:17

95

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Find a $x$ such that $2^{2015}x\equiv 1 \pmod{13}$

Published on 19 Nov 2018 - 16:38

77

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Find the remainder from the division of $3^{2017}-1$ into $3^{403}-1$

Published on 19 Nov 2018 - 18:31

25

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Prove $\phi(p^e)\not|p^et-1$

Published on 19 Nov 2018 - 20:10

146

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Some questions regarding the proof of Luroth theorem given by G. Bergman

Published on 20 Nov 2018 - 0:16

2.4k

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Find the smallest positive integer divisible by 63 such that the sum of its digits is also divisible by 63.

Published on 20 Nov 2018 - 8:10

54

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Find a $\tau(6n)$, if $\tau (2n)=28$ and $\tau (3n)=30$

Published on 21 Nov 2018 - 15:35

58

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Prove that number $4p^2+1$ can show as sum of squares of three different numbers

Published on 21 Nov 2018 - 16:23

2.1k

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Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$

Published on 26 Mar 2026 - 8:14

296

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If $2n+1$ and $3n+1$ are perfect squares, then prove that $8|n$.

Published on 21 Nov 2018 - 16:47

List Question

Prove that $2005|\underbrace{55 \ldots5}_{800\text{ digits}}$

proof that the sum of digits of natural number are divisible by 3 iff the number is

$2^{b}-1$ does not divide $2^{a}+1$

Infinite sequence $2^{n}-3 (n=2,3,...)$ contains no term divisible by 65

Checking if the Product of n Integers is Divisible by Prime N

How to prove an equivalence of two equations?

Find a $x$ such that $2^{2015}x\equiv 1 \pmod{13}$

Find the remainder from the division of $3^{2017}-1$ into $3^{403}-1$

Prove $\phi(p^e)\not|p^et-1$

Some questions regarding the proof of Luroth theorem given by G. Bergman

Find the smallest positive integer divisible by 63 such that the sum of its digits is also divisible by 63.

Find a $\tau(6n)$, if $\tau (2n)=28$ and $\tau (3n)=30$

Prove that number $4p^2+1$ can show as sum of squares of three different numbers

Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$

If $2n+1$ and $3n+1$ are perfect squares, then prove that $8|n$.

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