Discussion
Every natural number is :
Answer: A
Every natural number is a sum of distinct powers of 2.
This is the binary representation: every natural number \(n\) can be written uniquely as \(\sum b_{k}2^{k}\) with each \(b_{k} \in \{0, 1\}\), i.e. as a sum of distinct powers of 2. For example \(13 = 8 + 4 + 1\).
The others fail. 2 is not a sum of distinct powers of 3 (only 1, 3, 9, ... are available). 5 is not a sum of distinct factorials (1, 2, 6, ...): 1 + 2 = 3 and the next is 6. And 2 is not a sum of distinct triangular numbers (1, 3, 6, ...).
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