# A cyclic inequality with 4 variables

Algebra Level 5

$\large x^4y^2+y^4z^2+z^4t^2+t^4x^2+2016x^4y^4z^4t^4$

Let $$M$$ be the maximum value of the above expression for non-negative reals $$x,y,z,t$$ given $$x+y+z+t=1$$.

Given that $$M$$ can be expressed as $$\dfrac{a}{b}$$ where $$a, b$$ are positive integers and $$\gcd(a,b)=1$$.

Find $$a+b$$.

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