# What is the relation between Number Theory and Algebra Sets?

Let $$A_{2015}$$ be a set

$\large{A_{2015}=\{\ 2^{2015}-2^{k} | k \in Z, 0 \le k <2015\}\ }$

If the largest positive integer that cannot be written as the sum of one or more (not necessarily distinct) elements of $$A_{2015}$$ can be written as $$x\times 2^{y} +1$$. Find $$x+y$$ if both are integers

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