MathDB

24

Part of PEN K Problems

Problems(1)

K 24

Source:

5/25/2007
A function ff is defined on the positive integers by {f(1)=1,f(3)=3,f(2n)=f(n),f(4n+1)=2f(2n+1)−f(n),f(4n+3)=3f(2n+1)−2f(n),\left\{\begin{array}{rcl}f(1) &=& 1, \\ f(3) &=& 3, \\ f(2n) &=& f(n), \\ f(4n+1) &=& 2f(2n+1)-f(n), \\ f(4n+3) &=& 3f(2n+1)-2f(n), \end{array}\right. for all positive integers nn. Determine the number of positive integers nn, less than or equal to 1988, for which f(n)=nf(n) = n.
functioninductionFunctional Equations