MathDB
sequence of digits interlaced with another sequence of digit

Source: Romanian IMO TST 2005 - day 4, problem 4

April 23, 2005
modular arithmeticnumber theory proposednumber theory

Problem Statement

a) Prove that there exists a sequence of digits {cn}n≥1\{c_n\}_{n\geq 1} such that or each n≥1n\geq 1 no matter how we interlace knk_n digits, 1≤kn≤91\leq k_n\leq 9, between cnc_n and cn+1c_{n+1}, the infinite sequence thus obtained does not represent the fractional part of a rational number. b) Prove that for 1≤kn≤101\leq k_n\leq 10 there is no such sequence {cn}n≥1\{c_n\}_{n\geq 1}. Dan Schwartz
Back to ProblemsView on AoPS