Problem
ALG-B3-M05-P001 Additivity on Natural Numbers
#1
★★☆☆☆ Level 2 of 5
A function \(f:\mathbb N\to\mathbb R\) satisfies \(f(m+n)=f(m)+f(n)\) and \(f(1)=7\). Find \(f(n)\).
Use induction on \(n\).
The statement is true for \(n=1\). If \(f(n)=7n\), then \(f(n+1)=f(n)+f(1)=7n+7=7(n+1)\). Hence \(f(n)=7n\) for all \(n\in\mathbb N\).
Entry problem for the domain \(\mathbb N\).