An algebra problem by Abhay Kumar

Algebra Level 5

(a3+b3+c3)2(a4+b4+c4)(a5+b5+c5)2 \dfrac{(a^3+b^3+c^3)^2 (a^4+b^4+c^4)}{(a^5+b^5+c^5)^2}

Given a,ba, b and c c satisfy a+b+c=0 a + b + c = 0 and a5+b5+c50 a^5 + b^5 + c^5 \neq 0 , the value of the above expression can be expressed as mn\dfrac mn, where mm and nn are coprime positive integers, calculate the value of m+nm+n.

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