: 3 2 2 3 2 2
: 2. x + x y + xy + y = 8 ( x + xy + y + 1)
: 求 (x,y) 之所有整數解
令 x+y = a , xy = b
原式可改寫為 a^3 - 2ab = 8 (a^2-b+1)
→ a^3 - 8a^2 - 8 = 2ab - 8b
→ (a^3 - 8a^2 - 8) / a-4 = 2b
→ (a^2 - 4a - 16) - 72 / a-4 = 2b
然後開始討論，a-4 = ±72,36,24,18,12,9,8,6,4,3,2,1
a = 76 , b = 2727.5 不合
a = 40 , b = 711 x,y無解 ( 可用 (x-y)^2 = a^2-4b )
a = 28 , b = 326.5 不合
a = 22 , b = 188 x,y無解
a = 16 , b = 85 x,y無解
a = 13 , b = 51.5 不合
a = 12 , b = 30.5 不合
a = 10 , b = 16 (x,y) = (2,8)(8,2)
a = 8 , b = -1 x,y無解
a = 7 , b = -9.5 不合
a = 6 , b = -20 x,y無解
a = 5 , b = -41.5 不合
...
...
代完後可知道只有 (2,8) (8,2)
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