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January 30th, 2014, 11:13 AM   #1
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Diophantine equation

The diophantine equation :
x^5-5/16* x(x^2-y^2 )(3x^2+y^2 )=z^5
with x,y,z odd and gcd(x,y)=1, has no solutions.
How can you prove that ?
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