Question

Can I mix direct proof with inductive proof?

score 290 · Answer 1 · 2026-04-14 01:30:30

290

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Can I mix direct proof with inductive proof?

Published on 14 Apr 2026 - 1:30

score 708 · Answer 2 · 2026-04-15 05:58:27

708

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Nth derivative proof

Published on 15 Apr 2026 - 5:58

score 218 · Answer 3 · 2026-04-01 04:30:49

218

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Why would proving:$f \in PRC \rightarrow g(y,x_1,...,x_n)=\sum_{t=0}^yf(t,x_1,..,x_n)\in PRC$ by induction be wrong?

Published on 01 Apr 2026 - 4:30

score 833 · Answer 4 · 2026-04-15 05:32:14

833

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Prove that the integer $A= 3^{3n+3}- 36n - 27$ is divisible by $169$ for all positive integers $n$.

Published on 15 Apr 2026 - 5:32

score 1.5k · Answer 5 · 2026-04-16 05:33:02

1.5k

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Prove that $(1 + \sqrt2)^{2n} + (1 - \sqrt{2})^{2n}$ is an even integer.

Published on 16 Apr 2026 - 5:33

score 60 · Answer 6 · 2026-04-16 18:35:12

60

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Let $(a_n)_{n\geq 1}$ be a sequence of integers defined by $a_1=1, a_2=2$, and for each $n\geq 1$, $a_{n+2} =a_{n+1} +3a_n$.

Published on 16 Apr 2026 - 18:35

score 1.5k · Answer 7 · 2026-04-14 16:16:49

1.5k

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Prove Nth derivative expression by induction

Published on 14 Apr 2026 - 16:16

score 125 · Answer 8 · 2026-04-01 07:19:03

125

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Prove that $x_{n+1}=\frac{x_n}{2}+\frac{1}{x_n}\geq\sqrt{2}$

Published on 01 Apr 2026 - 7:19

score 63 · Answer 9 · 2026-04-11 11:26:41

63

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How can I prove this statement?

Published on 11 Apr 2026 - 11:26

score 526 · Answer 10 · 2026-04-16 13:42:29

526

Views

Show that for any natural number $n>24$ there exist natural numbers $p$ and $q$ such that $ n=5p+7q$

Published on 16 Apr 2026 - 13:42

score 62 · Answer 11 · 2026-04-10 17:06:27

62

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General Derivation and PMI--Why Bother?

Published on 10 Apr 2026 - 17:06

score 32 · Answer 12 · 2026-04-06 17:45:56

32

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Relation by induction

Published on 06 Apr 2026 - 17:45

score 50 · Answer 13 · 2026-04-14 13:34:06

50

Views

Induction over propositional variables

Published on 14 Apr 2026 - 13:34

score 47 · Answer 14 · 2026-04-17 03:48:12

47

Views

Proving a Fibonacci identity: $f_\ell = f_{m+1} \cdot f_{\ell-m} + f_m \cdot f_{\ell-(m+1)}$

Published on 17 Apr 2026 - 3:48

score 64 · Answer 15 · 2026-03-30 00:05:21

64

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The sum of integer parts of $2k/n$ over $k=1,\dots,n-1$

Published on 30 Mar 2026 - 0:05

List Question

Can I mix direct proof with inductive proof?

Nth derivative proof

Why would proving:$f \in PRC \rightarrow g(y,x_1,...,x_n)=\sum_{t=0}^yf(t,x_1,..,x_n)\in PRC$ by induction be wrong?

Prove that the integer $A= 3^{3n+3}- 36n - 27$ is divisible by $169$ for all positive integers $n$.

Prove that $(1 + \sqrt2)^{2n} + (1 - \sqrt{2})^{2n}$ is an even integer.

Let $(a_n)_{n\geq 1}$ be a sequence of integers defined by $a_1=1, a_2=2$, and for each $n\geq 1$, $a_{n+2} =a_{n+1} +3a_n$.

Prove Nth derivative expression by induction

Prove that $x_{n+1}=\frac{x_n}{2}+\frac{1}{x_n}\geq\sqrt{2}$

How can I prove this statement?

Show that for any natural number $n>24$ there exist natural numbers $p$ and $q$ such that $ n=5p+7q$

General Derivation and PMI--Why Bother?

Relation by induction

Induction over propositional variables

Proving a Fibonacci identity: $f_\ell = f_{m+1} \cdot f_{\ell-m} + f_m \cdot f_{\ell-(m+1)}$

The sum of integer parts of $2k/n$ over $k=1,\dots,n-1$

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