28 May 2008 00:57:08 IST
a1 = 2. a2 = 3, a3 = 7, a4 = 43
Now since
a(n+1) = an^2 - an + 1
and after a1, the next terms are odd...
so terms will be of the type
odd^2 - odd + 1
odd^2 is always odd... and odd^2 + 1 will become even.
then even - odd = odd always....
so there won't be any distinct pair with GCD = 6... 2 will be the only even number in the sequence.
Now since
a(n+1) = an^2 - an + 1
and after a1, the next terms are odd...
so terms will be of the type
odd^2 - odd + 1
odd^2 is always odd... and odd^2 + 1 will become even.
then even - odd = odd always....
so there won't be any distinct pair with GCD = 6... 2 will be the only even number in the sequence.