Equation Solution

2011-05-27 6:11 am
Are there any four natural numbers x,y,n,p to fit the equation?

x^n + y^n = p!

(n>0)
更新1:

I Need a detail proofing!

回答 (3)

2011-05-28 4:59 am
✔ 最佳答案
x = 12, y = 24, n = 2, p = 6
or
x = 24, n = 2, p = 6

12^2 + 24^2 = 6!
144 + 576 = 720
720 = 720

or

24^2 + 12^2 = 6!
576 + 144 = 720
720 = 720

There may be more, just two examples






2011-06-09 06:53:17 補充:
Forget to stay the value of y in the second solution (y =12)
x = 24, y = 12, n = 2, p = 6
2011-05-28 12:25 am
Sorry, One situation should be added

x<>y<>n<>p
2011-05-27 6:53 am
1^1 + 1^1 = 2!

x=y=n =1 , p=2

所以答案是肯定的


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