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List of triplets (Posted on 2016-10-21) Difficulty: 3 of 5
Determine all possible triplets (x, y,n) of positive integers,
fulfilling the equation:
(x+y)*(x−y)^ n = x*y

No Solution Yet Submitted by Ady TZIDON    
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re(3): solution Comment 4 of 4 |
(In reply to re(2): solution by Daniel)

if n is even then

(x-y)^n=(y-x)^n and thus my original solution still holds

if n is odd then
(x-y)^n=-(y-x)^n
if y>x then y-x>0 and -(y-x)^n<0
thus (x+y)(x-y)^n<0
but xy>0
thus there is still no solution

  Posted by Daniel on 2016-10-21 10:10:05
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