Question

$K = \mathbb{Z} / 2 \mathbb{Z}$. How many subspaces does the $K$-vector space $K^2$ have?

score 537 · Answer 1 · 2026-04-14 04:52:07

537

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$K = \mathbb{Z} / 2 \mathbb{Z}$. How many subspaces does the $K$-vector space $K^2$ have?

Published on 14 Apr 2026 - 4:52

score 4.1k · Answer 2 · 2026-04-14 02:19:34

4.1k

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The number of divisors being less than or equal to twice the square root of a natural number

Published on 14 Apr 2026 - 2:19

score 748 · Answer 3 · 2026-04-16 10:46:03

748

Views

Take a cube, add one, when is this a prime?

Published on 16 Apr 2026 - 10:46

score 53 · Answer 4 · 2026-04-16 08:38:54

53

Views

Prove that if $\\gcd(a,b)=1$ then $a\mathbb{N}\cap b\mathbb{N}=(ab)\mathbb{N}.$

Published on 16 Apr 2026 - 8:38

score 118 · Answer 5 · 2026-04-17 13:31:33

118

Views

Lost on introductory abstract algebra proof.

Published on 17 Apr 2026 - 13:31

score 131 · Answer 6 · 2026-04-12 19:49:03

131

Views

How can this step in an inductive proof by Paul Erdős be valid?

Published on 12 Apr 2026 - 19:49

score 2k · Answer 7 · 2026-04-17 15:13:44

2k

Views

Show that if $m \equiv 3 \mod 4$, then $m$ has a prime factor $p \equiv 3 \mod 4$.

Published on 17 Apr 2026 - 15:13

score 86 · Answer 8 · 2026-04-16 05:03:11

86

Views

Digit sum of $3k$ given the digit sums of $k$ and $44k$

Published on 16 Apr 2026 - 5:03

score 877 · Answer 9 · 2026-04-14 04:27:42

877

Views

If $n$ is such a positive integer, that $8|n^2$, then $4|n$

Published on 14 Apr 2026 - 4:27

score 99 · Answer 10 · 2026-04-13 10:31:43

99

Views

Binomial Coefficient Divisibility

Published on 13 Apr 2026 - 10:31

score 558 · Answer 11 · 2026-04-16 00:49:22

558

Views

Consider the equation $a_n +b_n\sqrt{2} = (1+\sqrt{2})^n$ where $a_n, b_n \in \mathbb{Z} \ge 1$. Prove that $\gcd(a_n, b_n) = 1$.

Published on 16 Apr 2026 - 0:49

score 72 · Answer 12 · 2026-04-11 13:37:33

72

Views

GCD as integral operator

Published on 11 Apr 2026 - 13:37

score 145 · Answer 13 · 2026-04-15 20:51:02

145

Views

Divisibility: 2 3 5 7 13 on $n^{13}-n$

Published on 15 Apr 2026 - 20:51

score 12.7k · Answer 14 · 2026-04-13 11:37:22

12.7k

Views

Any rectangular shape on a calculator numpad when divided by 11 gives an integer. Why?

Published on 13 Apr 2026 - 11:37

score 304 · Answer 15 · 2026-04-25 07:03:00

304

Views

Condition for Quintic Reciprocity

Published on 25 Apr 2026 - 7:03

List Question

$K = \mathbb{Z} / 2 \mathbb{Z}$. How many subspaces does the $K$-vector space $K^2$ have?

The number of divisors being less than or equal to twice the square root of a natural number

Take a cube, add one, when is this a prime?

Prove that if $\\gcd(a,b)=1$ then $a\mathbb{N}\cap b\mathbb{N}=(ab)\mathbb{N}.$

Lost on introductory abstract algebra proof.

How can this step in an inductive proof by Paul Erdős be valid?

Show that if $m \equiv 3 \mod 4$, then $m$ has a prime factor $p \equiv 3 \mod 4$.

Digit sum of $3k$ given the digit sums of $k$ and $44k$

If $n$ is such a positive integer, that $8|n^2$, then $4|n$

Binomial Coefficient Divisibility

Consider the equation $a_n +b_n\sqrt{2} = (1+\sqrt{2})^n$ where $a_n, b_n \in \mathbb{Z} \ge 1$. Prove that $\gcd(a_n, b_n) = 1$.

GCD as integral operator

Divisibility: 2 3 5 7 13 on $n^{13}-n$

Any rectangular shape on a calculator numpad when divided by 11 gives an integer. Why?

Condition for Quintic Reciprocity

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