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IMO Shortlist 1967 problem 2

1967 alg shortlist sustav
Find all real solutions of the system of equations:
\sum^n_{k=1} x^i_k = a^i for i = 1,2, \ldots, n.

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1967 alg shortlist sustav
2
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1967 alg shortlist sustav
0
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1967 alg shortlist sustav
0
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1984 alg shortlist sustav
0
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1986 alg shortlist sustav
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1