11
First,
We then
In fact,
Alright,
Because the question is modified,
9
We observe that
As we have x = 2^1234567, we can try to plug it in. We will use the prime factorization of the numbers to make things easier.
Next,
We notice that
This leaves us in the same place as the beginning, except
Because none of the denominators have a factor of 3,
We notice that
We see that
This means we just need to find the last 3 digits ...
4
Solution for b)
The answer is
Demonstration:
4
Partial Answer
Solution for a):
Process for a):
4
3
Yes, confirmed, here is how:
It remains to verify:
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