Problem
ALG-B1-M08-P003 Zero of an additive function
#3
★☆☆☆☆ Level 1 of 5
Let \(f(x+y)=f(x)+f(y)\) for all integers \(x,y\). Prove that \(f(0)=0\).
Substitute \(x=y=0\).
We get \(f(0)=f(0)+f(0)\). Subtracting \(f(0)\), we obtain \(f(0)=0\).
A basic start for the Cauchy equation.