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數學高手來~

Aug 18th 2013, 05:36

這是一個有趣題！！！

先假設 x = (5+3)(5^2+3^2)(5^4+3^4)(5^8+3^8) 是你想求的東西。

兩邊乘(5-3)。

(5-3)x = (5-3)(5+3)(5^2+3^2)(5^4+3^4)(5^8+3^8)
　　　= (5^2-3^2)(5^2+3^2)(5^4+3^4)(5^8+3^8)
　　　= (5^4-3^4)(5^4+3^4)(5^8+3^8)
　　　= (5^8-3^8)(5^8+3^8)
　　　= 5^16-3^16
　 2 x = 152544843904
　　x = 76272421952

或可答 x = (5^16-3^16)/2

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