Let's add

Probability Level 4

(20160)+(20164)+(20168)++(20162016)=x+x2.\dbinom{2016}{0}+\dbinom{2016}{4}+\dbinom{2016}{8}+\cdots +\dbinom{2016}{2016} = x+x^2.

If x=abx = a^b for positive integers aa and bb, find the smallest possible a+ba+b.

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