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Omni-MATH / A positive integer is called fancy if it can be expressed in the form…

Problem

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problem

A positive integer is called fancy if it can be expressed in the form 2a1+2a2+⋯+2a1002^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{100}} where a1,a2,…,a100a_{1}, a_{2}, \ldots, a_{100} are non-negative integers that are not necessarily distinct. Find the smallest positive integer nn such that no multiple of nn is a fancy number.
Plain-text mathematical notation (without MathML)
A positive integer is called fancy if it can be expressed in the form 2^(a₁)+2^(a₂)+⋯+2^(a₁₀₀) where a₁,a₂,…,a₁₀₀ are non-negative integers that are not necessarily distinct. Find the smallest positive integer n such that no multiple of n is a fancy number.
Original LaTeX notation
A positive integer is called fancy if it can be expressed in the form $$2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{100}}$$ where $a_{1}, a_{2}, \ldots, a_{100}$ are non-negative integers that are not necessarily distinct. Find the smallest positive integer $n$ such that no multiple of $n$ is a fancy number.

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Source and history

task_id
1dcd1d6b-a7c8-5e90-913e-66aad3abca34
task_key
test--1dcd1d6b-a7c8-5e90-913e-66aad3abca34
task_revision_id
1
config / split
/ test

Official source

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