a、b都是正整数,且满足a2-b2=2007,求a、b的值.(a平方-b平方=2007)

题目

a、b都是正整数,且满足a2-b2=2007,求a、b的值.(a平方-b平方=2007)

答案

a² - b² = 2007(a + b)(a - b) = 2007因为 2007 = 2007 × 1 = 669 × 3 = 223 × 9 所以a + b = 2007 ,a - b = 1 或 a + b = 669 ,a - b = 3 或 a + b = 223 ,a - b = 9解得：a = 1004b = 1003或a = 336b...