Question

Suppose $a,b\in\mathbb{Z}$. If $a^2(b^2-2b)$ is odd, then $a$ and $b$ are odd.

score 729 · Answer 1 · 2026-04-13 23:05:34

729

Views

Suppose $a,b\in\mathbb{Z}$. If $a^2(b^2-2b)$ is odd, then $a$ and $b$ are odd.

Published on 13 Apr 2026 - 23:05

score 1.5k · Answer 2 · 2026-04-15 15:45:11

1.5k

Views

If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$

Published on 15 Apr 2026 - 15:45

score 423 · Answer 3 · 2026-04-16 16:28:24

423

Views

Showing the composition of invertible functions $g \circ f$ is invertible with inverse $f^{-1} \circ g^{-1}$

Published on 16 Apr 2026 - 16:28

score 32 · Answer 4 · 2026-04-15 14:33:22

Right strategy to proof that $\forall b, c \in \mathbb{R}, b \gt 1: \exists n_0 \in \mathbb{N}: \forall n \ge n_0: n^c \le b^n$?

score 71 · Answer 5 · 2026-04-15 04:49:35

71

Views

Proving a formula for the amount of pendant nodes in a tree

Published on 15 Apr 2026 - 4:49

score 149 · Answer 6 · 2026-04-17 02:46:50

149

Views

Prove that $X\times Y=\emptyset$ $\iff$ $X=\emptyset$ or $Y=\emptyset$.

Published on 17 Apr 2026 - 2:46

score 49 · Answer 7 · 2026-04-16 01:03:20

49

Views

Show $f:\mathbb{R}\rightarrow\mathbb{R}$ $x\rightarrow -x$ is bijective

Published on 16 Apr 2026 - 1:03

score 57 · Answer 8 · 2026-04-12 14:19:36

57

Views

Proving a function is a fixed point

Published on 12 Apr 2026 - 14:19

score 41 · Answer 9 · 2026-04-16 07:46:36

41

Views

Proving $T^{n} \in \mathcal{L}(V, V), \forall n \in \mathbb{N}$.

Published on 16 Apr 2026 - 7:46

score 60 · Answer 10 · 2026-04-15 23:02:18

60

Views

Discrete mathematics Proof (∃y ∈ A, P y) ∨ (∃y ∈ A, Qy) =⇒ ∃x ∈ A, P x ∨ Qx with coq or by hand

Published on 15 Apr 2026 - 23:02

score 328 · Answer 11 · 2026-04-13 22:19:03

328

Views

To prove $\sup B = \inf A$

Published on 13 Apr 2026 - 22:19

score 209 · Answer 12 · 2026-04-16 11:48:13

209

Views

If $f:X\rightarrow Y$ is an order isomorphism , then $f^{-1}:Y\rightarrow X$ is an order isomorphism .

Published on 16 Apr 2026 - 11:48

score 2.1k · Answer 13 · 2026-04-15 20:37:48

2.1k

Views

Give a combinatorial proof of the following identity: $n^3 = n(n - 1)(n - 2) + 3n(n - 1) + n$

Published on 15 Apr 2026 - 20:37

score 48 · Answer 14 · 2026-04-15 12:30:02

48

Views

Formalising the equivalence of a (countably) infinite chain of "or"s and exists

Published on 15 Apr 2026 - 12:30

score 63 · Answer 15 · 2026-04-14 21:31:57

63

Views

Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

Published on 14 Apr 2026 - 21:31

List Question

Suppose $a,b\in\mathbb{Z}$. If $a^2(b^2-2b)$ is odd, then $a$ and $b$ are odd.

If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$

Showing the composition of invertible functions $g \circ f$ is invertible with inverse $f^{-1} \circ g^{-1}$

Right strategy to proof that $\forall b, c \in \mathbb{R}, b \gt 1: \exists n_0 \in \mathbb{N}: \forall n \ge n_0: n^c \le b^n$?

Proving a formula for the amount of pendant nodes in a tree

Prove that $X\times Y=\emptyset$ $\iff$ $X=\emptyset$ or $Y=\emptyset$.

Show $f:\mathbb{R}\rightarrow\mathbb{R}$ $x\rightarrow -x$ is bijective

Proving a function is a fixed point

Proving $T^{n} \in \mathcal{L}(V, V), \forall n \in \mathbb{N}$.

Discrete mathematics Proof (∃y ∈ A, P y) ∨ (∃y ∈ A, Qy) =⇒ ∃x ∈ A, P x ∨ Qx with coq or by hand

To prove $\sup B = \inf A$

If $f:X\rightarrow Y$ is an order isomorphism , then $f^{-1}:Y\rightarrow X$ is an order isomorphism .

Give a combinatorial proof of the following identity: $n^3 = n(n - 1)(n - 2) + 3n(n - 1) + n$

Formalising the equivalence of a (countably) infinite chain of "or"s and exists

Showing that, for $c,d\in\Bbb N$, $c|d$ implies $c\leq d$

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