$f:N \to Z | f(1)=0 $ and $n<m \Rightarrow f(n) < f(m)$. Prove $\forall x\in N$, there are unique $n,p \in N$ s.t $f(n) < x \leq f(n+1)$ x = f(n) + p.

score 324 · Answer 7 · 2026-03-25 07:44:41

324

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Is this a feasible way to show that a group $G$ is isomorphic to its opposite group $G^{op}$?

Published on 25 Mar 2026 - 7:44

score 285 · Answer 8 · 2026-04-15 14:58:52

285

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Proof by induction - Proving graph has a degree.

Published on 15 Apr 2026 - 14:58

score 448 · Answer 9 · 2026-04-15 18:55:48

448

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Prove $\forall n \in \mathbb {N}$, $6\vert (n^3-n)$. (strong induction)

Published on 15 Apr 2026 - 18:55

score 76 · Answer 10 · 2026-04-11 02:48:07

76

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fibonacci sequence induction with recurrence function

Published on 11 Apr 2026 - 2:48

score 153 · Answer 11 · 2026-04-16 22:02:20

153

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Prove that for all integers $a$ and $b$ and all $n \in \mathbb{N}, (a+b)\vert (a^{2n+1}+b^{2n+1})$ (induction)

Published on 16 Apr 2026 - 22:02

score 64 · Answer 12 · 2026-04-13 23:50:33

64

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Need help with RHS of Induction Problem about $1^{3} + 2^{3} + ... + n^{3}$ = $(1 + 2 + ... + n)^{2}$

Published on 13 Apr 2026 - 23:50

score 278 · Answer 13 · 2026-04-16 13:41:29

278

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Mathematical Induction with Exponents: $1 + \frac12 + \frac14 + \dots + \frac1{2^{n}} = 2 - \frac1{2^{n}}$

Published on 16 Apr 2026 - 13:41

score 9.6k · Answer 14 · 2026-04-16 02:09:04

9.6k

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Mathematical Induction and Divisibility $7\mid 11^n-4^n$

Published on 16 Apr 2026 - 2:09

score 112 · Answer 15 · 2026-04-12 00:11:15

112

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Mathematical Induction: how do I prove inequality

Published on 12 Apr 2026 - 0:11

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$f:N \to Z | f(1)=0 $ and $n<m \Rightarrow f(n) < f(m)$. Prove $\forall x\in N$, there are unique $n,p \in N$ s.t $f(n) < x \leq f(n+1)$ x = f(n) + p.

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