MathDB
Old Austrian

Source:

May 2, 2016
number theory

Problem Statement

For a positive integers n,kn,k we define k-multifactorial of n as Fk(n)Fk(n) = (n)(n) . (nk)(n-k) (n2k)(n-2k)...(r)(r), where rr is the reminder when nn is divided by kk that satisfy 1<=r<=k1<=r<=k Determine all non-negative integers nn such that F20(n)+2009F20(n)+2009 is a perfect square.