MathDB

22

Part of PEN M Problems

Problems(1)

M 22

Source:

5/25/2007
Let  a\, a, and b b \, be odd positive integers. Define the sequence {fn}n≥1\{f_n\}_{n\ge 1} by putting  f1=a,\, f_1 = a, f2=b, f_2 = b, \, and by letting  fn \, f_n \, for  n≥3 \, n \geq 3 \, be the greatest odd divisor of  fn−1+fn−2\, f_{n-1} + f_{n-2}. Show that  fn \, f_n \, is constant for sufficiently large  n \, n \, and determine the eventual value as a function of  a \, a \, and  b\, b.
functionRecursive Sequences