Question

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

score 210 · Answer 1 · 2026-03-26 04:35:09

210

Views

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

Published on 26 Mar 2026 - 4:35

score 66 · Answer 2 · 2018-09-25 06:22:02

66

Views

Induction for inequality

Published on 25 Sep 2018 - 6:22

score 2.5k · Answer 3 · 2018-09-25 09:00:02

2.5k

Views

Prove $\frac{d}{dx} x^n=nx^{n-1} : \forall n\in \mathbb{Z}_{+}$ by induction

Published on 25 Sep 2018 - 9:00

score 428 · Answer 4 · 2026-03-27 17:04:32

428

Views

Proving $\sum_{i=1}^{n} {{n}\choose{i}} (-1)^i = -1$ by induction

Published on 27 Mar 2026 - 17:04

score 834 · Answer 5 · 2018-09-25 18:31:35

834

Views

$\frac{d}{dx}x^n=nx^{n-1}$ proof by induction

Published on 25 Sep 2018 - 18:31

score 789 · Answer 6 · 2018-09-25 19:12:36

789

Views

Strong induction - prove that $n \le 3^\frac{n}3$ for every integer $n \ge 0$.

Published on 25 Sep 2018 - 19:12

score 93 · Answer 7 · 2018-09-26 01:09:51

93

Views

Proving $n \ge 41, \dfrac{2^{\lfloor\sqrt{2n}-3\rfloor}}{n} \ge 1$ without using derivatives

Published on 26 Sep 2018 - 1:09

score 68 · Answer 8 · 2018-09-26 05:17:03

68

Views

Polynomial Length upper bound

Published on 26 Sep 2018 - 5:17

score 514 · Answer 9 · 2026-03-26 04:34:51

514

Views

Finding $f(9999)$ if $f(1) = 2$ and $f(mn) = f(m) \, f(n) - f(m+n) + 1001$ for $m$ or $n$ equal to $1$

Published on 26 Mar 2026 - 4:34

score 590 · Answer 10 · 2026-03-25 19:01:39

590

Views

Equivalence Induction and Well-Ordering

Published on 25 Mar 2026 - 19:01

score 3.4k · Answer 11 · 2026-03-26 11:05:30

3.4k

Views

$a-b$ divides $a^n-b^n$

Published on 26 Mar 2026 - 11:05

score 95 · Answer 12 · 2026-03-26 09:15:00

95

Views

Induction where statement has different cases

Published on 26 Mar 2026 - 9:15

score 40 · Answer 13 · 2018-09-28 01:09:45

40

Views

Show inequality holds by induction

Published on 28 Sep 2018 - 1:09

score 188 · Answer 14 · 2018-09-28 01:27:04

188

Views

Help on using structural induction for set equality

Published on 28 Sep 2018 - 1:27

score 67 · Answer 15 · 2018-09-28 17:16:11

67

Views

Let $n\in\mathbb{Z}^+$, and let $p$ be a prime number. Prove by induction that $n^p$ can be expressed as the sum of $n$ and some multiple of $p$.

Published on 28 Sep 2018 - 17:16

List Question

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

Induction for inequality

Prove $\frac{d}{dx} x^n=nx^{n-1} : \forall n\in \mathbb{Z}_{+}$ by induction

Proving $\sum_{i=1}^{n} {{n}\choose{i}} (-1)^i = -1$ by induction

$\frac{d}{dx}x^n=nx^{n-1}$ proof by induction

Strong induction - prove that $n \le 3^\frac{n}3$ for every integer $n \ge 0$.

Proving $n \ge 41, \dfrac{2^{\lfloor\sqrt{2n}-3\rfloor}}{n} \ge 1$ without using derivatives

Polynomial Length upper bound

Finding $f(9999)$ if $f(1) = 2$ and $f(mn) = f(m) \, f(n) - f(m+n) + 1001$ for $m$ or $n$ equal to $1$

Equivalence Induction and Well-Ordering

$a-b$ divides $a^n-b^n$

Induction where statement has different cases

Show inequality holds by induction

Help on using structural induction for set equality

Let $n\in\mathbb{Z}^+$, and let $p$ be a prime number. Prove by induction that $n^p$ can be expressed as the sum of $n$ and some multiple of $p$.

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