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由 thepiano »
易知 a ≠ b
由於對稱,先設 a > b
(3b - 1) / a < (3a - 1) / a = 3 - 1/a < 3
故
(1) 3b - 1 = a
(3a - 1) / b = (9b - 4) / b = 9 - 4/b 為整數
b = 4,a = 11
(2) 3b - 1 = 2a
(3a - 1) / b = (9b/2 - 5/2) / b = (9b - 5) / (2b) = 4 + [(b - 5) / (2b)] 為整數
b = 5,a = 7
所求 = 4 + 5 + 7 + 11