All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 LCM Sequence (Posted on 2006-08-19)
Let's look at the sequence with terms a1=19, a2=95, and an+2=LCM(an+1,an)+an

LCM stands for Least Common Multiple, and n is a positive integer.

Find the Greatest Common Divisor (GCD) of terms a4096 and a4097.

 No Solution Yet Submitted by atheron Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(3): Just a guess... -- proof | Comment 4 of 7 |
(In reply to re(2): Just a guess... -- proof by Richard)

Yes, that's what I'm saying: that any factor of a(n+2) and a(n+1) is a factor of a(n), as a(n+2) = a(n)*(u2+1), where u2 is LCM(a(n),a(n+1))/a(n) and so contains the factors of a(n+1) that are not factors of a(n).  Adding 1 to this in forming a factor of a(n+2) prevents n+2 from having factors common to a(n+1) that are not factors of a(n).

 Posted by Charlie on 2006-08-19 19:18:23

 Search: Search body:
Forums (0)