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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Prove that the equation $2^a - 2^b - 1=3^c$ has no integral solution with $a,b\geq 3$

I was looking for a natural power of 3 that could be written like Binary format: 11..(N times)..11011..(M times)..11 Example: 1111110111111111111111 (...isn't a power of 3) Or could also be written …
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