整数a、b满足ab=4a+4b-3,求满足条件的数组(a,b)
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由 ab = 4a + 4b - 3
ab - 4a = 4b - 3
a(b - 4) = 4b - 3
a = ( 4b - 3)/(b - 4)
= (4b - 16 + 13 )/(b - 4)
= 4 + 13/(b - 4)
根据题意:a是整数,所以,13/(b - 4) 一定为整数
则有 b - 4 = ±1 或 b - 4 = ±13
当b - 4 = 1 b = 5, a = 17, 此时满足条件的数组是(17,5)
当 b - 4 = -1时, b = 3 a = - 9, 此时满足条件的数组是(-9, 3)
当 b - 4 = 13时, b = 17, a = 5, 此时满足条件的数组是(5,17)
当 b - 4 = -13时, b = -9, a = 3, 此时满足条件的数组是(3 ,-9)
ab - 4a = 4b - 3
a(b - 4) = 4b - 3
a = ( 4b - 3)/(b - 4)
= (4b - 16 + 13 )/(b - 4)
= 4 + 13/(b - 4)
根据题意:a是整数,所以,13/(b - 4) 一定为整数
则有 b - 4 = ±1 或 b - 4 = ±13
当b - 4 = 1 b = 5, a = 17, 此时满足条件的数组是(17,5)
当 b - 4 = -1时, b = 3 a = - 9, 此时满足条件的数组是(-9, 3)
当 b - 4 = 13时, b = 17, a = 5, 此时满足条件的数组是(5,17)
当 b - 4 = -13时, b = -9, a = 3, 此时满足条件的数组是(3 ,-9)
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