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Omni-MATH / Determine all sequences (x₁,x₂,…,x₂₀₁₁) of positive integers, such that for every positive integer n there exists an integer a with ∑_(j=1)²⁰¹¹jx_(j)^(n)=a^(n+1)+1 [i]

Problem

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problem

Determine all sequences (x1,x2,…,x2011)(x_1,x_2,\ldots,x_{2011}) of positive integers, such that for every positive integer nn there exists an integer aa with ∑j=12011jxjn=an+1+1\sum^{2011}_{j=1} j x^n_j = a^{n+1} + 1 [i]
Plain-text mathematical notation (without MathML)
Determine all sequences (x₁,x₂,…,x₂₀₁₁) of positive integers, such that for every positive integer n there exists an integer a with ∑_(j=1)²⁰¹¹jx_(j)^(n)=a^(n+1)+1

[i]
Original LaTeX notation
Determine all sequences $(x_1,x_2,\ldots,x_{2011})$ of positive integers, such that for every positive integer $n$ there exists an integer $a$ with \[\sum^{2011}_{j=1} j  x^n_j = a^{n+1} + 1\]

[i]

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Source and history

task_id
560b48a1-3191-578d-9cca-f734995b5245
task_key
test--560b48a1-3191-578d-9cca-f734995b5245
task_revision_id
1
config / split
/ test

Official source

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