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Clearly and so throughout we suppose that both x is greater than 1 but less than 30. This leaves 28 such values left to be computed. We begin by computing at powers of two. Since
we see that a equals 2 is an admissable value. Further, we immediately get that
and so for b ranging from 1 to 4 we see that a can take on the values 2,4,8 or 16. This covers the x values .
Next for x equals , notice that
which gives us an already chosen a value. Using these facts, we can clearly see that
Further at x equals ,
and this value was also an already chosen a value. I claim that these values are enough to show that all admissable values of a have already been found. To see this, notice for example that
and the right hand side was already shown to be a power of 2. Similarly
is also a power of 2. Crunching through the remaining cases, we have
and in all these cases, we have already shown the right hand side to be a power of 2. Thus the admissable values for a are given by .
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