But 2016 isn't here yet!

Algebra Level 3

Evaluate the expression 20164+20162+120163+1\large {\frac{2016^{4}+2016^{2}+1}{2016^{3}+1}} .

If the answer can be expressed as a mixed fraction in simplest form abca \frac{b}{c} , find a+b+c.a+b+c.


Note: Solve this problem without using a calculator.

Hobart Pao by Hobart Pao
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