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Let $S=\{1,2,3,4,5....,2070\}$ and $A$ be the number of subsets of $S$ whose sum of elements in $S$ is divisible by $9$.If $$A=\frac{2^a\left(2^b+1\right)}{c}$$then find the values of $a,b$ and $c$.

The given solution is quite cryptic:

Let $f(x)=(1+x)(1+x^2)(1+x^3)....(1+x^{2070})$.

Then $A$ must be the sum of coefficient of $x^{9k}$ where $k$ is non-negative integer.So, $$A=\frac{2^{2070}+8.2^{230}}{9}$$How has the author of this question calculated this expression

Maverick
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    I just posted a new answer there which attempts to answer your questions. My answer differs from the one the author had, but I am pretty certain I am correct. – Mike Earnest May 02 '19 at 16:08

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