ILL 1984 Problem 28

A "number triangle" $(t_{n, k}) (0 \le k \le n)$ is defined by $t_{n,0} = t_{n,n} = 1 (n \ge 0),$ $$t_{n+1,m} =(2 -\sqrt{3})^mt_{n,m} +(2 +\sqrt{3})^{n-m+1}t_{n,m-1} (1 \le m \le n)$$ Prove that all $t_{n,m}$ are integers.