Let's look at the sequence with terms
a
1=19,
a
2=95, and a
n+2=LCM(a
n+1,a
n)+a
n
LCM stands for Least Common Multiple, and n is a positive integer.
Find the Greatest Common Divisor (GCD) of terms a4096 and a4097.
(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).
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Posted by Charlie
on 2006-08-19 19:18:23 |
re(3): Just a guess... -- proof
