MathDB
Numbers increasing, greatest divisors decreasing

Source: All-Russian Olympiad 2006 finals, problem 10.5 = 9.5

May 7, 2006
number theory proposednumber theory

Problem Statement

Let a1a_1, a2a_2, ..., a10a_{10} be positive integers such that a1<a2<...<a10a_1<a_2<...<a_{10}. For every kk, denote by bkb_k the greatest divisor of aka_k such that bk<akb_k<a_k. Assume that b1>b2>...>b10b_1>b_2>...>b_{10}. Show that a10>500a_{10}>500.
Back to ProblemsView on AoPS