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Omni-MATH / Determine which integers n>1 have the property that there exists an infinite sequence a₁ , a₂ , a₃ , … of nonzero integers such that the equality a_(k)+2a_(2k)+…+na_(nk)=0 holds fo…

Problem

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problem

Determine which integers n>1n > 1 have the property that there exists an infinite sequence a1a_1 , a2a_2 , a3a_3 , …\dots of nonzero integers such that the equality ak+2a2k+…+nank=0a_k + 2a_{2k} + \dots + na_{nk} = 0 holds for every positive integer kk .
Plain-text mathematical notation (without MathML)
Determine which integers n>1 have the property that there exists an infinite sequence a₁ , a₂ , a₃ , … of nonzero integers such that the equality a_(k)+2a_(2k)+…+na_(nk)=0 holds for every positive integer k .
Original LaTeX notation
Determine which integers $n > 1$ have the property that there exists an infinite sequence $a_1$ , $a_2$ , $a_3$ , $\dots$ of nonzero integers such that the equality \[a_k + 2a_{2k} + \dots + na_{nk} = 0\] holds for every positive integer $k$ .

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Source and history

task_id
342ec622-6298-554c-b54e-d2cca6fb8819
task_key
test--342ec622-6298-554c-b54e-d2cca6fb8819
task_revision_id
1
config / split
/ test

Official source

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