Powerful numbers (4,8,9,16,25,27... )are defined as follows: if a prime p divides n then p² must also divide n.
(8,9) is a couple of two consecutive numbers,both of them being powerful.
Find another pair(s) like that.

The more the merrier!!

(In reply to re: An interesting remark ***** Spoiler by Daniel)

1.Of course, it is obvious.  That's why the sentence begins:...it is easy to see...etc

2.It is not "my discovery" - I've quoted the source.

3. There is a small typo in the  4th row of your post, which should read:      . "  .now it remains to show that 4n(n+1)+1
is also a p.n. "

You may still edit it.

Posted by Ady TZIDON on 2010-08-09 20:13:29