Consider a sequence {a(n)} with a(1) = 2 and a(n) = (a(n-1))²/a(n-2) for all n ≥ 3.

It is known that a(2) and a(5) are positive integers and a(5) ≤ 2012.

What are the possible values of a(5)?

For all k and the mth term:2k^(m-1), for any k and m>0; 2^(2-m)*k^(m-1), for any k and m<2;

Hence the solutions sought are:

a(2) = {2,4,6,8,10},

a(5)={2,32,162,512,1250}

Edited on March 14, 2012, 10:51 am

Posted by broll on 2012-03-14 10:48:50