Problem

Source: Iran Third Round 1997, E1, P3

Tags: algebra unsolved, algebra



Find all sets of real numbers $\{a_1,a_2,\ldots, _{1375}\}$ such that \[2 \left( \sqrt{a_n - (n-1)}\right) \geq a_{n+1} - (n-1), \quad \forall n \in \{1,2,\ldots,1374\},\] and \[2 \left( \sqrt{a_{1375}-1374} \right) \geq a_1 +1.\]