perplexus.info :: Just Math : List of triplets

List of triplets (Posted on 2016-10-21)

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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