# Don't Overthink It

Number Theory Level 5

$\large{ 2^{a+1} - 2^a + 2 = \ 2^b - 2^c }$

Evaluate the sum of the sums of all ordered tuples of integers $$(a,b,c)$$ that exist as solutions to the equation above.

Details and Assumptions:

• $$a, b,$$ and $$c$$ are neither necessarily distinct nor positive.

• The "sum of a tuple" is the sum of its members.

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