MathDB

1

Part of 2017 European Mathematical Cup

Problems(2)

Diophantine eq.

Source: European Mathematical Cup 2017

1/3/2018
Solve in integers the equation : x2y+y2=x3x^2y+y^2=x^3
number theory
Functional inequality on N

Source: European Mathematical Cup 2017 Problem 1

12/27/2017
Find all functions f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} such that the inequality f(x)+yf(f(x))≤x(1+f(y))f(x)+yf(f(x))\le x(1+f(y)) holds for all positive integers x,yx, y.
Proposed by Adrian Beker.
functional equationinequalitiesNatural Numbers