Question

Proof by induction with a prime number

score 1.4k · Answer 1 · 2016-08-25 21:29:02

1.4k

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Proof by induction with a prime number

Published on 25 Aug 2016 - 21:29

score 1k · Answer 2 · 2026-04-05 01:10:28

1k

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Prove by mathematical induction that $31\mid5^{n+1}+6^{2n-1},\;$ $\forall n \in \mathbb{N}$

Published on 05 Apr 2026 - 1:10

score 61 · Answer 3 · 2026-04-12 15:30:48

How, by proving for a particular choice of $a_n$ in induction proof of AM-GM, we conclude the inequality for all $a_n \in \mathbb{R}$ ?

score 66 · Answer 4 · 2016-08-27 06:01:28

66

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Fibonacci Sequence. Proof via induction

Published on 27 Aug 2016 - 6:01

score 105 · Answer 5 · 2016-08-27 15:10:15

105

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Induction: Negation for Even Integers implies Negation for all Integers?

Published on 27 Aug 2016 - 15:10

score 251 · Answer 6 · 2026-04-12 16:57:53

251

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Roots of Polynomial by Induction

Published on 12 Apr 2026 - 16:57

score 111 · Answer 7 · 2026-04-09 14:39:42

111

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Help with proof by induction problem

Published on 09 Apr 2026 - 14:39

score 72 · Answer 8 · 2016-08-29 23:15:12

72

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Prove $\sum_{i=1}^n{(-1)^{i(i-1)/2}}$ is bounded

Published on 29 Aug 2016 - 23:15

score 86 · Answer 9 · 2026-04-12 16:57:52

86

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Prove the inequality using induction

Published on 12 Apr 2026 - 16:57

score 168 · Answer 10 · 2016-08-30 03:40:11

168

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Prove by induction that ${x}^{2k}-{y}^{2k}=(x+y)t$ for all natural numbers $k$ and $t$.

Published on 30 Aug 2016 - 3:40

score 78 · Answer 11 · 2016-08-30 06:50:11

78

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Mathematical induction and sequences $1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots+\frac{1}{1+2+\dots+n}=\frac{2n}{n+1}$

Published on 30 Aug 2016 - 6:50

score 46 · Answer 12 · 2026-04-12 10:01:05

46

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Provide a logical translation of "There are at least n objects" in $L_=$

Published on 12 Apr 2026 - 10:01

score 244 · Answer 13 · 2026-03-29 15:02:28

244

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What is an inductive proof that every set is either infinite, in bijection with a subset of $\mathbb{N}$, or empty?

Published on 29 Mar 2026 - 15:02

score 239 · Answer 14 · 2026-04-12 08:13:19

239

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Munkres's Strong induction principle vs. "traditional" mathematical induction

Published on 12 Apr 2026 - 8:13

score 2.8k · Answer 15 · 2026-04-12 07:52:43

2.8k

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Prove that $4^n+ 1$ is not divisible by $3$

Published on 12 Apr 2026 - 7:52

List Question

Proof by induction with a prime number

Prove by mathematical induction that $31\mid5^{n+1}+6^{2n-1},\;$ $\forall n \in \mathbb{N}$

How, by proving for a particular choice of $a_n$ in induction proof of AM-GM, we conclude the inequality for all $a_n \in \mathbb{R}$ ?

Fibonacci Sequence. Proof via induction

Induction: Negation for Even Integers implies Negation for all Integers?

Roots of Polynomial by Induction

Help with proof by induction problem

Prove $\sum_{i=1}^n{(-1)^{i(i-1)/2}}$ is bounded

Prove the inequality using induction

Prove by induction that ${x}^{2k}-{y}^{2k}=(x+y)t$ for all natural numbers $k$ and $t$.

Mathematical induction and sequences $1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots+\frac{1}{1+2+\dots+n}=\frac{2n}{n+1}$

Provide a logical translation of "There are at least n objects" in $L_=$

What is an inductive proof that every set is either infinite, in bijection with a subset of $\mathbb{N}$, or empty?

Munkres's Strong induction principle vs. "traditional" mathematical induction

Prove that $4^n+ 1$ is not divisible by $3$

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