Question

A beautiful mathematical induction problem: $11 \mid 1+2^{2^n}+3^{2^n}+4^{2^n}+5^{2^n}$

score 172 · Answer 1 · 2026-04-17 13:29:27

172

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A beautiful mathematical induction problem: $11 \mid 1+2^{2^n}+3^{2^n}+4^{2^n}+5^{2^n}$

Published on 17 Apr 2026 - 13:29

score 139 · Answer 2 · 2026-04-11 13:03:37

139

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Can every statement that can be proved using the well-ordering principle be proved using weak mathematical induction?

Published on 11 Apr 2026 - 13:03

score 75 · Answer 3 · 2026-04-08 22:47:50

75

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Does anyone know of any application of mathematical induction in Complex Analysis?

Published on 08 Apr 2026 - 22:47

score 74 · Answer 4 · 2026-04-11 05:21:34

74

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Is it possible to prove the Taylor Series by mathematical induction?

Published on 11 Apr 2026 - 5:21

score 125 · Answer 5 · 2026-04-13 06:51:10

125

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Mathematical induction in a limit problem

Published on 13 Apr 2026 - 6:51

score 67 · Answer 6 · 2026-04-14 01:22:48

67

Views

Trigonometric indentity proof by induction?

Published on 14 Apr 2026 - 1:22

score 71 · Answer 7 · 2026-04-15 10:56:55

71

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Show that the recursive sequence $x_{k+1} = |x_k - \frac{x_k}{1-2M^2x_k^2}|$ is monotone

Published on 15 Apr 2026 - 10:56

score 183 · Answer 8 · 2026-04-15 04:47:56

183

Views

Prove the following by induction: Every natural number n > 6 can be written as n = 3j + 4k for some integers j and k

Published on 15 Apr 2026 - 4:47

score 118 · Answer 9 · 2026-04-14 20:38:39

118

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$\displaystyle \int \sin^{n}(x)dx$ by induction

Published on 14 Apr 2026 - 20:38

score 56 · Answer 10 · 2026-04-14 19:00:02

56

Views

Proof by induction $uf(n)+f(n-1)=g(n)\equiv 0\pmod x \implies f(n)\equiv 0\pmod x$

Published on 14 Apr 2026 - 19:00

score 100 · Answer 11 · 2026-04-13 09:33:58

100

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Evaluating the infinite sum of $n^k/n!$

Published on 13 Apr 2026 - 9:33

score 34 · Answer 12 · 2026-04-11 13:12:17

34

Views

Proving equivalence of two different induction definitions

Published on 11 Apr 2026 - 13:12

score 46 · Answer 13 · 2026-04-12 02:31:05

46

Views

Tree with no vertices of degree 2 has more leaves than non-leaves

Published on 12 Apr 2026 - 2:31

score 128 · Answer 14 · 2026-04-17 05:10:54

128

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Any positive integer can be written as $2^{\sum_{k=1}^N n_k+m_k}+\sum_{i=1}^{N} 2^{\left(\sum_{k=i}^N n_k+m_{k+1}\right)}\left(2^{m_i}-1\right)$

Published on 17 Apr 2026 - 5:10

score 70 · Answer 15 · 2026-04-12 20:59:06

70

Views

Induction Proof for the Sum of the First n Fibonacci Numbers

Published on 12 Apr 2026 - 20:59

List Question

A beautiful mathematical induction problem: $11 \mid 1+2^{2^n}+3^{2^n}+4^{2^n}+5^{2^n}$

Can every statement that can be proved using the well-ordering principle be proved using weak mathematical induction?

Does anyone know of any application of mathematical induction in Complex Analysis?

Is it possible to prove the Taylor Series by mathematical induction?

Mathematical induction in a limit problem

Trigonometric indentity proof by induction?

Show that the recursive sequence $x_{k+1} = |x_k - \frac{x_k}{1-2M^2x_k^2}|$ is monotone

Prove the following by induction: Every natural number n > 6 can be written as n = 3j + 4k for some integers j and k

$\displaystyle \int \sin^{n}(x)dx$ by induction

Proof by induction $uf(n)+f(n-1)=g(n)\equiv 0\pmod x \implies f(n)\equiv 0\pmod x$

Evaluating the infinite sum of $n^k/n!$

Proving equivalence of two different induction definitions

Tree with no vertices of degree 2 has more leaves than non-leaves

Any positive integer can be written as $2^{\sum_{k=1}^N n_k+m_k}+\sum_{i=1}^{N} 2^{\left(\sum_{k=i}^N n_k+m_{k+1}\right)}\left(2^{m_i}-1\right)$

Induction Proof for the Sum of the First n Fibonacci Numbers

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