a、b都是正整数,且满足a2-b2=2007,求a - 知识问答

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)

3个回答

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 = 1004
b = 1003
或
a = 336
b = 333
或
a = 116
b = 107

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