# Welcome 2016! Part 11

**Algebra**Level 5

Is there any infinite sequence of real numbers \(a_{1}\),\(a_{2}\), \(a_{3} \ldots\) such that

\[\large a_{1}^{m} + a_{2}^m + a_{3}^m \ldots \ = \ m \]

for every positive integer \(m\) ?

Is there any infinite sequence of real numbers \(a_{1}\),\(a_{2}\), \(a_{3} \ldots\) such that

\[\large a_{1}^{m} + a_{2}^m + a_{3}^m \ldots \ = \ m \]

for every positive integer \(m\) ?

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