x+y+z=3,x^3+y^3+z^3=15,x^4+y^4+z^4=35,x^5+y^5+z^5=
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EDIT: By nontrivial I mean no 0's. (Credits to Slade for reminding me to define this)
EDIT2: In fact, you are free to find a nontrivial solution to (3n−3)(x2+y2+z2)=(9n+1)(xy+yz+zx)where n≡1(mod5) is a positive integer. The one I posted above is the case n=5(2)+1, but you will make my day if you can find a nontrivial solution for any n=5k+1.
EDIT2: In fact, you are free to find a nontrivial solution to (3n−3)(x2+y2+z2)=(9n+1)(xy+yz+zx)where n≡1(mod5) is a positive integer. The one I posted above is the case n=5(2)+1, but you will make my day if you can find a nontrivial solution for any n=5k+1.
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