2 To The Ten Is 2 High

Number Theory Level pending

How many $$20$$-element subsets of $$\{0,1,2,...,1024\}$$ can be ordered to form a geometric progression modulo $$1025$$ with common ratio $$2?$$

Details and assumptions

The sequence $$\{a_i \}$$ is a geometric progression modulo $$1025$$ with common ratio $$2$$ if $$a_i \equiv a_1 \times 2^{i-1} \pmod{1025}$$.

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