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# 3.3 Divisibility rules revisited

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Thinking out Loud

Can any integer $$n$$ be written as a sum of distinct powers of $$2$$?

Example $$\PageIndex{1}$$:

Express $$2019$$ as a sum of distinct powers of $$2$$?

Note that, $$10 \equiv 1 ( mod 3), 10 \equiv 1 ( mod 9),$$ and $$10 \equiv (-1)( mod 11),$$.

Divisible by 3

The probabilities assigned to events by a distribution function on a sample space are given by.

Proof

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