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APMO 1995 - Asian Pacific Mathematics Olympiad Question 1

APMO · APMO 1995 - Asian Pacific Mathematics Olympiad

Question 1

Determine all real sequences $a_1,a_2,\ldots,a_{1995}$ satisfying
$$2\sqrt{a_n-(n-1)}\ge a_{n+1}-(n-1)\qquad(n=1,2,\ldots,1994),$$
and $2\sqrt{a_{1995}-1994}\ge a_1+1$.