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Find all sets of real numbers

Source: Iran Third Round 1997, E1, P3

March 27, 2011
algebra unsolvedalgebra

Problem Statement

Find all sets of real numbers {a1,a2,…,1375}\{a_1,a_2,\ldots, _{1375}\} such that 2 \left( \sqrt{a_n - (n-1)}\right) \geq a_{n+1} - (n-1),   \forall n \in \{1,2,\ldots,1374\}, and 2(a1375−1374)≥a1+1.2 \left( \sqrt{a_{1375}-1374} \right) \geq a_1 +1.
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