Problem
ALG-B3-M06-P003 Shifted Sum on Natural Numbers
#3
★★☆☆☆ Level 2 of 5
A function \(f:\mathbb N\to\mathbb Z\) satisfies \(f(m+n)=f(m)+f(n)+1\) and \(f(1)=4\). Find \(f(n)\).
Put \(g(n)=f(n)+1\).
Then \(g(m+n)=f(m+n)+1=f(m)+f(n)+2=g(m)+g(n)\). On \(\mathbb N\), \(g(n)=ng(1)=5n\). Hence \(f(n)=5n-1\).
A shift on a discrete domain.