Question

A function f:ZxZ -> Z defined as f(m,n)=3n-4m.

How would I show this is surjective?

Answer 1

\[f(3-k,4-k)=3(4-k)-4(3-k)=12-3k-12+4k=k\]

Answer 2

then for any \(k\in\mathbb{Z}\) we have \(f(3-k,4-k)=k\)

Answer 3

awesome, thanks!

Answer 4

np