167
161
165
163

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$(2^x)^2 - 13 \cdot 2^x + 1 = 0$ $2^a + 2^b = 13, \; 2^a \cdot 2^b = 1$ $(2^a)^2 + (2^b)^2 = (2^a + 2^b )^2 - 2 \cdot 2^a \cdot 2^b$ $\boxed{4^a + 4^b = 167}$