小品3味 - 拼圖

1 3 8 120 X

X = A^2-1
3X = B^2-1
8X = C^2-1
120X = D^2-1

3A^2-2 = B^2 (1)
8A^2-7 = C^2 (2)
120A^2-119 = D^2 (3)

(2)-(1) => 5A^2-5 = C^2-B^2
(3)-(1) => 117A^2-117 = D^2-B^2

117(C^2-B^2) = 5(D^2-B^2)
117C^2 = 112B^2+5D^2 (D>C>B>1 ,正整數)

算到這裡

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