Let's look at the sequence with terms
=95, and an+2
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 Just a guess...
by Dej Mar)
LCM(a(n),a(n+1)) = GCD(a(n),a(n+1)) * u1 * u2,
where u1 is a(n)/gcd and u2 is a(n+1)/gcd.
a(n+2) = GCD(a(n),a(n+1)) * u1 * u2 + a(n)
= a(n) * u2 + a(n)
= a(n) *(u2 + 1)
The only gcd this shares with a(n+1) is the same GCD(a(n),a(n+1)) as u2+1 can't chare common divisors with u2, and a(n+1) is in fact just GCD(a(n),a(n+1)) * u2.
This confirms 19 as the answer.
Posted by Charlie
on 2006-08-19 16:21:41