# Don't Overthink It

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

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.

Bonus: For extra fun, consider the same question but with the equation $$2^{a+1}-2^a+1=2^b-2^c$$.

×