初中数学竞赛中,经常出现一类融一元二次方程与质数于一体的题目.解决这类题目关键是根据题目特点,灵活将一元二次方程的有关知识与质数的特殊性质,结合起来求解.下面以若干典型试题为例,谈谈这类试题的基本类型及其解法. In junior mathematics competitions, there is often a class of problems involving the integration of one-dimensional quadratic equations with prime numbers. The key to solving such problems is to combine the knowledge about the quadratic equation of one yuan and the special properties of prime numbers flexibly. The following takes a number of typical questions as an example to talk about the basic types of these questions and their solutions.