2/a + 3/b = 1 <==> (2b+3a)/(ab) = 1 <==> ab-3a-2b=0
<==> (a-2)(b-3) = 6.
a, b 為整數, 所以 a-2, b-3 亦為整數.
xy = 6 的整數解:
1×6 即 x=1, y=6 或 x=6 y=1, 則 a=3, b=9 或 a=8, b=4.
2×3 即 x=2, y=3 或 x=3, y=2, 則 a=4, b=6 或 a=5, b=5.
(-1)×(-6) 即 x=-1, y=-6 或 x=-6, y=-1, 則 a=1, b=-3 或 a=-4, b=2.
(-2)×(-3) 即 x=-2, y=-3 或 x=-3, y=-2, 前者需 a=0 不符,
後者得 a=-1, b=1.
故: 限於正整數解, 則有 (3,9), (8,4), (4,6) 及 (5,5) 共4組;
若不限正整數, 則加 (1,-3), (-4,2) 及 (-1,1) 三組, 合計 7組解.
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