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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