解題 ---(2025•广东)《九章算术》是世界上较早给出勾股公式的著作, 掌握确定勾股数组的方法对研究直角三角形具有重要意义. 若直角三角形的三边长 a, b, c 都是正整数, 则 a, b, c 为一组“勾股数”. 如表中的每一组数都是勾股数. Table: The image contains a table with 4 rows and 5 columns. Each cell contains a set of three numbers, representing a Pythagorean triple (勾股数). Table Content: | 3, 4, 5 | 7, 24, 25 | 11, 60, 61 | 15, 112, 113 | 19, 180, 181 | | 4, 3, 5 | 8, 15, 17 | 12, 35, 37 | 16, 63, 65 | 20, 21, 29 | | 5, 12, 13 | 9, 12, 15 | 13, 84, 85 | 17, 144, 145 | 21, 28, 35 | | 6, 8, 10 | 10, ___, 26 | 14, 48, 50 | 18, 80, 82 | 22, 120, 122 | Question (1): (1) 请补全如表中的勾股数. (1) Please complete the Pythagorean triple in the table. Question (2): (2) 根据如表中数据规律, 用含字母 (均为正整数) 的代数式分别表示 a, b, c, 使该组代数式能表示上表中的所有的勾股数, 并证明. (2) According to the data pattern in the table, use algebraic expressions containing letters (all positive integers) to represent a, b, c respectively, so that this set of algebraic expressions can represent all Pythagorean triples in the table, and prove it.