List questions from divisibility

Published on 12 Apr 2026 - 16:34

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What is the multiplicative order of $1+\sqrt{2}$?

Published on 27 Mar 2026 - 12:14

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Prove that neither $A$ nor $B$ is divisible by $5$

Published on 12 Apr 2026 - 0:43

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Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$

Published on 03 Apr 2026 - 2:36

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Is this assertion about g.c.d. true?

Published on 12 Apr 2026 - 6:06

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Divisibility proofs for greatest common divisor

Published on 03 Apr 2026 - 2:33

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Permutations where no partial sum is divisible by 3 (contest question)

Published on 12 Apr 2026 - 6:35

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If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?

Published on 14 Aug 2015 - 0:54

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Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?

Published on 12 Apr 2026 - 7:15

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Is there a Divisibility Metric for Numbers?

Published on 12 Apr 2026 - 7:06

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Find all integers such that $2 < x < 2014$ and $2015|(x^2-x)$

Published on 17 Aug 2015 - 0:48

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$\gcd (ca, cb) = \gcd (a, b)c$ if $c > 0$

Published on 03 Apr 2026 - 2:33

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$\gcd(ca,cb)\mid ca$ and $\gcd(ca,cb)\mid cb \to \gcd(ca,cb)\mid cd$.

Published on 18 Aug 2015 - 1:05

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Is there a name for the least exponent $e$ such that a power of an integer is divisible by another?

Published on 11 Apr 2026 - 16:18

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If $2xy$ divides $x^2+y^2-x$, prove that $x$ is a perfect square

Published on 01 Apr 2026 - 0:28

List Question

divisibility relations in sets.

What is the multiplicative order of $1+\sqrt{2}$?

Prove that neither $A$ nor $B$ is divisible by $5$

Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$

Is this assertion about g.c.d. true?

Divisibility proofs for greatest common divisor

Permutations where no partial sum is divisible by 3 (contest question)

If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?

Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?

Is there a Divisibility Metric for Numbers?

Find all integers such that $2 < x < 2014$ and $2015|(x^2-x)$

$\gcd (ca, cb) = \gcd (a, b)c$ if $c > 0$

$\gcd(ca,cb)\mid ca$ and $\gcd(ca,cb)\mid cb \to \gcd(ca,cb)\mid cd$.

Is there a name for the least exponent $e$ such that a power of an integer is divisible by another?

If $2xy$ divides $x^2+y^2-x$, prove that $x$ is a perfect square

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