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Algebra Level 4

If r=1rr4+r2+1=11a \displaystyle \sum_{r=1}^\infty \dfrac r{r^4+r^2+1} = 1 - \dfrac1a , find the number of digits in a2016a^{2016} .

You are given the following approximations: log10=1,log5=0.6990,log3=0.4771\log 10 = 1, \log 5 = 0.6990, \log 3 = 0.4771 .

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