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AUSTRIAN-POLISH 1995 Problem 1

    Determine all real solutions (a1,...,an)(a_1,...,a_n) of the following system of equations: {a3=a2+a1a4=a3+a2...an=an−1+an−2a1=an+an−1a2=a1+an\begin{cases}a_3 = a_2 + a_1 a_4 = a_3 + a_2 ... a_n = a_{n-1} + a_{n-2} a_1= a_n +a_{n-1} a_2 = a_1 + a_n \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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