1987年全国高中数学联赛第一试有这样一道填空题:若 k 是大于1的整数,a 是方程 x~2-kx+1=0的根,对于大于10的任意自然数 n,a~2~n+a~(-2)~n的个位数字总是7,则 k 的个位数字是____.我们把思路放宽一些来考虑,设 a_n=a~2~n+ In 1987, the first test of the National High School Mathematical League Match had the following question: If k is an integer greater than 1, a is the root of the equation x~2-kx+1=0, and for any natural number n greater than 10, a~2~ The single-digit number of n+a~(-2)~n is always 7, then the single-digit number of k is ____. Let’s consider a little bit of relaxation and let a_n=a~2~n+