List questions from divisibility

Published on 12 Apr 2026 - 9:57

60

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$a,b$ be two positive integers , where $b>2 $ , then is it possible that $2^b-1 \mid 2^a+1$?

Published on 06 Sep 2015 - 13:04

55

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Does there exist positive integers $a,b,n$ , where $n>1$ , such that $a^n - b^n |a^n + b^ n$ ?

Published on 06 Sep 2015 - 14:06

1.3k

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Suppose $a$, $b$, and $c$ are integers. Prove that if $a \mid b$ and $a \mid c$, then $a \mid (b +c)$

Published on 12 Apr 2026 - 20:54

111

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Is it possible for $(900q^2+ap^2)/(3q^2+b^2p^2)$ to be an integer?

Published on 12 Apr 2026 - 12:39

53

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Show that 2|n(n+1) using induction

Published on 07 Sep 2015 - 13:47

215

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Systems of linear modular equations with unknowns in the moduli

Published on 12 Apr 2026 - 9:34

114

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$1+2^x+\ldots+n^x \mid 1+2^y+\ldots+n^y$ for all $n$ implies $x=y$?

Published on 26 Mar 2026 - 7:59

58

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Prove that $2\mid x$ and $5\mid x$ if and only if $10\mid x$

Published on 09 Sep 2015 - 3:09

244

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$n^2 + 7n + 1$ is odd

Published on 30 Mar 2026 - 14:26

85

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Proof for elementary divisibility problem

Published on 08 Apr 2026 - 23:49

216

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Is it correct that $\frac{1}{0}=\frac{1}{-0}$ and if it is, why is $\frac{1}{0} \neq 0$?

Published on 10 Sep 2015 - 18:37

64

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$2(n-2)+1$ does not divide $(n-2)(n-3)/2$ for $n \ge 8$

Published on 11 Sep 2015 - 18:35

173

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Euclid's proof on the infinity of primes

Published on 12 Apr 2026 - 11:44

117

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Show that there exist infinitely many $i$ such that $a_i-1$ is divisible by $2^{2015}$

Published on 12 Apr 2026 - 20:33

List Question

Prove $p$ is prime

$a,b$ be two positive integers , where $b>2 $ , then is it possible that $2^b-1 \mid 2^a+1$?

Does there exist positive integers $a,b,n$ , where $n>1$ , such that $a^n - b^n |a^n + b^ n$ ?

Suppose $a$, $b$, and $c$ are integers. Prove that if $a \mid b$ and $a \mid c$, then $a \mid (b +c)$

Is it possible for $(900q^2+ap^2)/(3q^2+b^2p^2)$ to be an integer?

Show that 2|n(n+1) using induction

Systems of linear modular equations with unknowns in the moduli

$1+2^x+\ldots+n^x \mid 1+2^y+\ldots+n^y$ for all $n$ implies $x=y$?

Prove that $2\mid x$ and $5\mid x$ if and only if $10\mid x$

$n^2 + 7n + 1$ is odd

Proof for elementary divisibility problem

Is it correct that $\frac{1}{0}=\frac{1}{-0}$ and if it is, why is $\frac{1}{0} \neq 0$?

$2(n-2)+1$ does not divide $(n-2)(n-3)/2$ for $n \ge 8$

Euclid's proof on the infinity of primes

Show that there exist infinitely many $i$ such that $a_i-1$ is divisible by $2^{2015}$

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