Question

Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

score 2.5k · Answer 1 · 2026-03-26 14:33:59

2.5k

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Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

Published on 26 Mar 2026 - 14:33

score 263 · Answer 2 · 2026-03-25 17:36:37

263

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How can we express "induction is the same as recursion", formally?

Published on 25 Mar 2026 - 17:36

score 105 · Answer 3 · 2026-03-26 21:14:01

105

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Prove for any $\sum_{i=1}^n f_i^2 = f_n \times f_{n+1}$ using Fibonacci numbers

Published on 26 Mar 2026 - 21:14

score 653 · Answer 4 · 2026-03-28 10:19:24

653

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Is calculus of inductive constructions more powerful than calculus of constructions?

Published on 28 Mar 2026 - 10:19

score 100 · Answer 5 · 2026-03-26 20:44:24

100

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How to use induction to prove this Lemma?

Published on 26 Mar 2026 - 20:44

score 68 · Answer 6 · 2026-03-27 05:38:07

68

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How do you prove $\prod_{i=0}^n(1+2^{2^i})=2^{2^{n+1}}-1$ using induction?

Published on 27 Mar 2026 - 5:38

score 46 · Answer 7 · 2019-07-04 19:48:44

46

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Proof by induction. Let $f(0)=1$ and $f(n+1)= (n+1)f(n)$. Prove $f(n)=n(n-1)(n-2)...(2)(1)$

Published on 04 Jul 2019 - 19:48

score 73 · Answer 8 · 2026-03-27 11:45:28

73

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How do you prove this recursive formula?

Published on 27 Mar 2026 - 11:45

score 261 · Answer 9 · 2019-07-05 10:07:21

261

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How do I prove that the set of rational functions is closed under composition by structural induction?

Published on 05 Jul 2019 - 10:07

score 60 · Answer 10 · 2019-07-05 22:28:33

60

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Proof by induction of the Euclide formula

Published on 05 Jul 2019 - 22:28

score 72 · Answer 11 · 2019-07-08 20:38:51

72

Views

Prove $\sum_{i=n}^{2n}i=\frac{3}{2}n(n+1)$ using induction

Published on 08 Jul 2019 - 20:38

score 124 · Answer 12 · 2026-03-27 07:14:26

124

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$n^n<(n-1)^{n+1}$ for integer $n\ge5$

Published on 27 Mar 2026 - 7:14

score 51 · Answer 13 · 2026-03-28 02:10:38

51

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Prove that there are $(n-1)!$ possible cyclic orders of $n$ objects

Published on 28 Mar 2026 - 2:10

score 677 · Answer 14 · 2026-03-26 22:14:48

677

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Question regarding this proof that a nonempty binary tree with n nodes has height at least $\lfloor log_2 n\rfloor$.

Published on 26 Mar 2026 - 22:14

score 175 · Answer 15 · 2019-07-10 02:15:31

175

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Is there a version of induction that can be used for decreasing negative numbers?

Published on 10 Jul 2019 - 2:15

List Question

Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

How can we express "induction is the same as recursion", formally?

Prove for any $\sum_{i=1}^n f_i^2 = f_n \times f_{n+1}$ using Fibonacci numbers

Is calculus of inductive constructions more powerful than calculus of constructions?

How to use induction to prove this Lemma?

How do you prove $\prod_{i=0}^n(1+2^{2^i})=2^{2^{n+1}}-1$ using induction?

Proof by induction. Let $f(0)=1$ and $f(n+1)= (n+1)f(n)$. Prove $f(n)=n(n-1)(n-2)...(2)(1)$

How do you prove this recursive formula?

How do I prove that the set of rational functions is closed under composition by structural induction?

Proof by induction of the Euclide formula

Prove $\sum_{i=n}^{2n}i=\frac{3}{2}n(n+1)$ using induction

$n^n<(n-1)^{n+1}$ for integer $n\ge5$

Prove that there are $(n-1)!$ possible cyclic orders of $n$ objects

Question regarding this proof that a nonempty binary tree with n nodes has height at least $\lfloor log_2 n\rfloor$.

Is there a version of induction that can be used for decreasing negative numbers?

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