# A mind boggling question

Algebra Level pending

For positive real numbers $a,b,c$ which of the following statements necessarily implies $a = b = c$

$(I). a(b^{3}+c^{3})=b(a^{3}+c^{3})=c(a^{3}+b^{3})$ $(II). a(a^{3}+b^{3})=b(b^{3}+c^{3})=c(c^{3}+a^{3})$

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