  A function $f$ from $\mathbb{Z}$ to the symmetric matrices over an arbitrary
field $K$ of characteristic $0$ is a $1$-quasihomomorphism if the matrix
$f(x+y) - f(x) - f(y)$ has rank at most $1$ for all $x,y \in \mathbb{Z}$. We
show that any such $1$-quasihomomorphism has distance at most $2$ from an
actual group homomorphism. This gives a positive answer to a special case of a
problem posed by Kazhdan and Ziegler.
