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RMO 2025 K1

  • KV and JNV
  1. Solve the following system of equations in nonnegative integers a1,a2,…,a8a_1, a_2, \ldots, a_8 where ai≠1a_i \ne 1 for i=1,…,8i=1, \ldots, 8 : \begin{align*} a_1 a_2 &= a_3 + a_4 a_3 a_4 &= a_5 + a_6 a_5 a_6 &= a_7 + a_8 a_7 a_8 &= a_1 + a_2 \end{align*}

Dataset text AI-MO AoPS. Quoted with source.

Official text: Indian Regional Mathematical Olympiad 2025 official paper, page 1.

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