Question

Solving Functional Equation with an essence of Number Theory

score 135 · Answer 1 · 2026-04-09 00:24:51

135

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Solving Functional Equation with an essence of Number Theory

Published on 09 Apr 2026 - 0:24

score 99 · Answer 2 · 2026-04-17 07:52:21

99

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Find all functions $f:\mathbb R \rightarrow \mathbb R$ that have following two properties

Published on 17 Apr 2026 - 7:52

score 37 · Answer 3 · 2026-04-11 22:23:33

37

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Engineering a convergent sum over all integer combinations of $1$ and $\pi$

Published on 11 Apr 2026 - 22:23

score 48 · Answer 4 · 2026-04-15 20:11:47

48

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Find all Function $f:\mathbb R \rightarrow \mathbb R$ such that $f(x+yf(x))=f(x)+xf(y) \; \forall \; x,y \in \mathbb R$

Published on 15 Apr 2026 - 20:11

score 235 · Answer 5 · 2026-04-09 02:20:10

235

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Solving functional equations using recursion

Published on 09 Apr 2026 - 2:20

score 60 · Answer 6 · 2026-04-09 14:58:02

60

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A functional equation problem with an interesting pattern

Published on 09 Apr 2026 - 14:58

score 74 · Answer 7 · 2026-04-16 08:18:18

74

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Solve for $f(y)$ in $\int_0^{\infty} f (y) \cos{(y x)}\,\mathrm{d}y = \dfrac{1}{\sqrt{x}}$

Published on 16 Apr 2026 - 8:18

score 80 · Answer 8 · 2026-04-15 18:41:31

80

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How to solve the functional equation $f(s,t) - sf(t,1) - tf(s,1) + tsf(1,1) = s(1-t)$

Published on 15 Apr 2026 - 18:41

score 384 · Answer 9 · 2026-04-14 00:10:30

384

Views

Solving the functional equation: $f\bigl(f(x)-x\bigr)=2x$

Published on 14 Apr 2026 - 0:10

score 194 · Answer 10 · 2026-04-16 19:06:31

194

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Find all function $f:\mathbb Q^+ \rightarrow \mathbb Q^+$ that satisfy $f(x)+f\bigg(\dfrac{1}{x}\bigg)=1$ and $f(2x+1)=\dfrac{f(x)}{2}$

Published on 16 Apr 2026 - 19:06

score 105 · Answer 11 · 2026-04-10 11:41:06

105

Views

Linear iterative functional equation always has a solution

Published on 10 Apr 2026 - 11:41

score 104 · Answer 12 · 2026-04-11 01:38:29

104

Views

Given a functional equation with the following data. Prove this problem

Published on 11 Apr 2026 - 1:38

score 113 · Answer 13 · 2026-04-17 11:08:01

113

Views

Show that there are infinitely many functions $f:\mathbb N\rightarrow\mathbb N$ satisfying $f(2)=2$ and$f(mn)=f(m)f(n) \forall m,n\in \mathbb N$

Published on 17 Apr 2026 - 11:08

score 194 · Answer 14 · 2026-04-16 07:53:41

194

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Let $ f: ( 0, \infty) \rightarrow ( 0, \infty)$ bijective with $ f^{-1}(x) \cdot f(x) =1$.

Published on 16 Apr 2026 - 7:53

score 169 · Answer 15 · 2026-04-16 03:23:29

169

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$f(f(x - y)) = f(x) f(y) - f(x) + f(y) - xy$

Published on 16 Apr 2026 - 3:23

List Question

Solving Functional Equation with an essence of Number Theory

Find all functions $f:\mathbb R \rightarrow \mathbb R$ that have following two properties

Engineering a convergent sum over all integer combinations of $1$ and $\pi$

Find all Function $f:\mathbb R \rightarrow \mathbb R$ such that $f(x+yf(x))=f(x)+xf(y) \; \forall \; x,y \in \mathbb R$

Solving functional equations using recursion

A functional equation problem with an interesting pattern

Solve for $f(y)$ in $\int_0^{\infty} f (y) \cos{(y x)}\,\mathrm{d}y = \dfrac{1}{\sqrt{x}}$

How to solve the functional equation $f(s,t) - sf(t,1) - tf(s,1) + tsf(1,1) = s(1-t)$

Solving the functional equation: $f\bigl(f(x)-x\bigr)=2x$

Find all function $f:\mathbb Q^+ \rightarrow \mathbb Q^+$ that satisfy $f(x)+f\bigg(\dfrac{1}{x}\bigg)=1$ and $f(2x+1)=\dfrac{f(x)}{2}$

Linear iterative functional equation always has a solution

Given a functional equation with the following data. Prove this problem

Show that there are infinitely many functions $f:\mathbb N\rightarrow\mathbb N$ satisfying $f(2)=2$ and$f(mn)=f(m)f(n) \forall m,n\in \mathbb N$

Let $ f: ( 0, \infty) \rightarrow ( 0, \infty)$ bijective with $ f^{-1}(x) \cdot f(x) =1$.

$f(f(x - y)) = f(x) f(y) - f(x) + f(y) - xy$

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