Question

Find all functions $f$ such that for all positive integers $x$, $y$, $f(xy)+f(x+y)=f(x)f(y)+1$.

score 380 · Answer 1 · 2020-04-08 18:32:34

380

Views

Find all functions $f$ such that for all positive integers $x$, $y$, $f(xy)+f(x+y)=f(x)f(y)+1$.

Published on 08 Apr 2020 - 18:32

score 130 · Answer 2 · 2020-04-09 12:18:14

130

Views

Find all function such that : $f(x+1)=x^{3}-f(x-1)$.

Published on 09 Apr 2020 - 12:18

score 387 · Answer 3 · 2020-04-10 13:04:24

387

Views

Find all functions $f$ such that for any rationals $x$ and $y$, $f(x+y)=f(x)f(y)-f(xy)+1$.

Published on 10 Apr 2020 - 13:04

score 125 · Answer 4 · 2020-04-11 05:36:10

125

Views

Find all continuous functions $ f(x+y)=\frac{f(x)+f(y)+2 f(x) f(y)}{1-f(x) f(y)} $

Published on 11 Apr 2020 - 5:36

score 70 · Answer 5 · 2020-04-11 12:52:21

70

Views

What are the continuous functions $ x f(y)+y f(x)=(x+y) f(x) f(y) ? $

Published on 11 Apr 2020 - 12:52

score 666 · Answer 6 · 2020-04-11 18:50:06

666

Views

Function with the property $f(a+b)=f(a)+f(b)+2ab$

Published on 11 Apr 2020 - 18:50

score 206 · Answer 7 · 2020-04-12 05:41:43

206

Views

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(m+n)=f(m)+f(n)+2 m n$

Published on 12 Apr 2020 - 5:41

score 82 · Answer 8 · 2020-04-13 05:34:39

82

Views

Functional equations Question from Olympiad book

Published on 13 Apr 2020 - 5:34

score 93 · Answer 9 · 2020-04-13 11:03:21

93

Views

Find all $f$ such that $ 2 f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2} $

Published on 13 Apr 2020 - 11:03

score 76 · Answer 10 · 2020-04-13 15:00:12

Proving surjectivity from $f\Bigl(\bigl(x+f(x)\bigr)^2\Bigr) = \bigl(x+f(x)\bigr)^2$ in a functional equation problem

score 289 · Answer 11 · 2020-04-14 04:51:01

289

Views

Find all $f$ such that $f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2},$

Published on 14 Apr 2020 - 4:51

score 60 · Answer 12 · 2020-04-14 11:10:38

60

Views

Find all $f:Z→Z$ which satisfy $f(m+n)(f(m)−f(n))=f(m−n)(f(m)+f(n))$

Published on 14 Apr 2020 - 11:10

score 149 · Answer 13 · 2026-03-27 00:55:08

149

Views

Doubt in IMO 1982 problem 1

Published on 27 Mar 2026 - 0:55

score 415 · Answer 14 · 2026-03-25 17:21:53

415

Views

Cauchy's functional equation with bounds: $ a \le f ( x ) + f ( y ) - f ( x + y ) \le b $

Published on 25 Mar 2026 - 17:21

score 283 · Answer 15 · 2020-04-16 12:43:59

Continuous functions satisfying $f(f(x))=x$, for all $x \in \mathbb{R}$, and $\int_{-x}^{0} f(t)dt - \int_{0}^{x^2}f(t)dt=x^3$ for $x>0$

List Question

Find all functions $f$ such that for all positive integers $x$, $y$, $f(xy)+f(x+y)=f(x)f(y)+1$.

Find all function such that : $f(x+1)=x^{3}-f(x-1)$.

Find all functions $f$ such that for any rationals $x$ and $y$, $f(x+y)=f(x)f(y)-f(xy)+1$.

Find all continuous functions $ f(x+y)=\frac{f(x)+f(y)+2 f(x) f(y)}{1-f(x) f(y)} $

What are the continuous functions $ x f(y)+y f(x)=(x+y) f(x) f(y) ? $

Function with the property $f(a+b)=f(a)+f(b)+2ab$

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(m+n)=f(m)+f(n)+2 m n$

Functional equations Question from Olympiad book

Find all $f$ such that $ 2 f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2} $

Proving surjectivity from $f\Bigl(\bigl(x+f(x)\bigr)^2\Bigr) = \bigl(x+f(x)\bigr)^2$ in a functional equation problem

Find all $f$ such that $f\left(m^{2}+n^{2}\right)=f(m)^{2}+f(n)^{2},$

Find all $f:Z→Z$ which satisfy $f(m+n)(f(m)−f(n))=f(m−n)(f(m)+f(n))$

Doubt in IMO 1982 problem 1

Cauchy's functional equation with bounds: $ a \le f ( x ) + f ( y ) - f ( x + y ) \le b $

Continuous functions satisfying $f(f(x))=x$, for all $x \in \mathbb{R}$, and $\int_{-x}^{0} f(t)dt - \int_{0}^{x^2}f(t)dt=x^3$ for $x>0$

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