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Omni-MATH / Let X_(r)=x^(r)+y^(r)+z^(r) with x,y,z real. It is known that if S₁=0, (*)quadfracS_m+nm+n=fracS_mmfracS_nn for (m,n)=(2,3),(3,2),(2,5), or (5,2). Determine [i]all[/i… · Discussion

Discussing Let X_(r)=x^(r)+y^(r)+z^(r) with x,y,z real. It is known that if S₁=0, (*)quadfrac{S_{m+n}}{m+n}=frac{S_m}{m}frac{S_n}{n} for (m,n)=(2,3),(3,2),(2,5), or (5,2). Determine [i]all[/i… · Omni-MATH

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