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Omni-MATH / Let n be a positive integer. Find, with proof, the least positive integer d_(n) which cannot be expressed in the form ∑_(i=1)^(n)(−1)^(a_(i))2^(b_(i)), where a_(i) and b_(i) are no…

Problem

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problem

Let

n

be a positive integer. Find, with proof, the least positive integer

d_{n}

which cannot be expressed in the form

\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},

where

a_{i}

and

b_{i}

are nonnegative integers for each

i.

Plain-text mathematical notation (without MathML)

Let n be a positive integer. Find, with proof, the least positive integer d_(n) which cannot be expressed in the form ∑_(i=1)^(n)(−1)^(a_(i))2^(b_(i)),
where a_(i) and b_(i) are nonnegative integers for each i.

Original LaTeX notation

Let $n$ be a positive integer. Find, with proof, the least positive integer $d_{n}$ which cannot be expressed in the form \[\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},\]
where $a_{i}$ and $b_{i}$ are nonnegative integers for each $i.$

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task_id: bcfca5e1-7312-5391-bb97-34da4b6c133a
task_key: test--bcfca5e1-7312-5391-bb97-34da4b6c133a
task_revision_id: 4
config / split: / test

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