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LCM Sequence (Posted on 2006-08-19) Difficulty: 3 of 5
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)

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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
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