List questions from divisibility

Published on 31 May 2019 - 4:49

79

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Prove that if $2\mid n$ or $8\mid (n-1)$...

Published on 31 May 2019 - 12:41

271

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Show that $x^n -1 \mid x^k -1 \Leftrightarrow n \mid k$

Published on 01 Jun 2019 - 10:43

331

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In $\mathbb Z[\sqrt D]$, how do I see if there are no elements of a certain norm?

Published on 01 Jun 2019 - 11:40

180

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For every sufficiently large $m$ there exists $k$ such that $m = k + \tau(k)$

Published on 25 Mar 2026 - 11:13

261

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Solve for $x$ and $y$, $(\sqrt x+\sqrt 3)^2=y+6\sqrt 2$

Published on 05 Jun 2019 - 18:03

94

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Given that $a$ and $b$ are integers satisfied $3 \mid ab(a + b) + 2$, prove that $9 \mid ab(a + b) + 2$.

Published on 06 Jun 2019 - 10:39

103

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Prove that $n$ is Divisible by $6$ when the Quadratics have integer roots

Published on 06 Jun 2019 - 17:35

193

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Solve $x^2y^2 - 4x^2y + y^3 + 4x^2 - 3y^2 + 1 = 0$ over the integers.

Published on 09 Jun 2019 - 16:30

830

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Solve for integer $m,n$: $2^m = 3^n + 5$

Published on 09 Jun 2019 - 17:51

89

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Alternative Solutions to “American Billions” like puzzles: Find a 9-digit number (no repeats), where the first digits give a number divisible by

Published on 09 Jun 2019 - 20:20

330

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Condition for the sum of two fractions to be irreducible

Published on 27 Mar 2026 - 8:46

812

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Prove that $6|a+b+c $ if and only if $6|a^3 +b^3+c^3$

Published on 10 Jun 2019 - 9:03

466

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Rational numbers modulo $p$ for some prime $p$

Published on 25 Mar 2026 - 17:36

128

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Find the positive integers pair $(x, y)$ such that $xy^2 + y + 1 \mid x^2y + x + y$.

Published on 11 Jun 2019 - 16:13

List Question

Why 16 and any odd integer are relatively prime?

Prove that if $2\mid n$ or $8\mid (n-1)$...

Show that $x^n -1 \mid x^k -1 \Leftrightarrow n \mid k$

In $\mathbb Z[\sqrt D]$, how do I see if there are no elements of a certain norm?

For every sufficiently large $m$ there exists $k$ such that $m = k + \tau(k)$

Solve for $x$ and $y$, $(\sqrt x+\sqrt 3)^2=y+6\sqrt 2$

Given that $a$ and $b$ are integers satisfied $3 \mid ab(a + b) + 2$, prove that $9 \mid ab(a + b) + 2$.

Prove that $n$ is Divisible by $6$ when the Quadratics have integer roots

Solve $x^2y^2 - 4x^2y + y^3 + 4x^2 - 3y^2 + 1 = 0$ over the integers.

Solve for integer $m,n$: $2^m = 3^n + 5$

Alternative Solutions to “American Billions” like puzzles: Find a 9-digit number (no repeats), where the first digits give a number divisible by

Condition for the sum of two fractions to be irreducible

Prove that $6|a+b+c $ if and only if $6|a^3 +b^3+c^3$

Rational numbers modulo $p$ for some prime $p$

Find the positive integers pair $(x, y)$ such that $xy^2 + y + 1 \mid x^2y + x + y$.

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