New posts in functional-equations

Solutions of $f(x+y^{n})=f(x)+[f(y)]^{n}$.

functional-equations

Existence of a function

functional-equations

If $f: \Bbb{N} \to \Bbb{N}$ is strictly increasing and $f(f(n))=3n$, find $f(2001)$. [duplicate]

functions functional-equations

Find $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(2x^2+2yf(z))=2xf(x)+2zf(y).$

algebra-precalculus functional-equations

A BDMO functional equation problem.

contest-math recreational-mathematics problem-solving functional-equations

Find all polynomials $p$ such that $p(x+1)=p(x)+2x+1.$

functions polynomials functional-equations

Factoring x + y

functional-equations

The functional equation $f(x)+f(y)+f(z)+f(x+y+z)=f(x+y)+f(y+z)+f(z+x)$

calculus functional-equations

Finding functions satisfying $f(f(x))+f(x)+x=0$

functional-equations

Problem on Euler's Phi function

number-theory functional-equations totient-function

Solving $f'(x) = f(f(x))$ [duplicate]

ordinary-differential-equations functional-equations

Finding all polynomials $P(x) \in \mathbb R[x]$ such that $P(x)^2=4P\left(x^2-5x+1\right)+2$

algebra-precalculus polynomials functional-equations

Finding all functions $f:\mathbb{R}\to\mathbb{R}$ such that $f\bigl(xf(x+y)\bigr)=f\bigl(yf(x)\bigr)+x^2$

contest-math functional-equations

If $B(x+y)-B(x)-B(y)\in\mathbb Z$ can we add an integer function to $B$ to make it additive?

algebra-precalculus functions functional-equations

Is there a less-trivial integer function with described properties?

functional-equations integers semiring

Is this $f(x) = x+1$ the only solution to this functional equation.

functional-equations

Functional equation $4f(x^2+y^2)=(f(x)+f(y))^2$

algebra-precalculus recreational-mathematics functional-equations

Characterizing the solutions of the functional equation $ f ( 3 x ) - f ( 2 x ) = f ( 2 x ) - f ( x ) $

functional-equations

Determine all functions $f$ on $\mathbb R$ such that $f(x^2+yf(x))=f(x)f(x+y)$ for all $x,y$

contest-math functional-equations

About the solution of the infinite recurrence $f(x,f(x,f(x,f(x,f(...))))=a$

functions convergence-divergence functional-equations