MathDB
Sequence x_{n+2} = gcd( x_{n+1} , x_{n} ) + 2006

Source: XV Rioplatense Mathematical Olympiad (2006), Level 3

August 10, 2011
number theorygreatest common divisornumber theory unsolved

Problem Statement

An infinite sequence x1,x2,…x_1,x_2,\ldots of positive integers satisfies xn+2=gcd⁡(xn+1,xn)+2006 x_{n+2}=\gcd(x_{n+1},x_n)+2006 for each positive integer nn. Does there exist such a sequence which contains exactly 10200610^{2006} distinct numbers?
Back to ProblemsView on AoPS