"Larry Hammick" <larryhammick@[EMAIL PROTECTED]
> wrote:
>
> Anyhow, here's a proof of IX.20 discovered by Filip Saidak in 2005 AD!
> Define inductively a sequence (x(n), y(n)) of ordered pairs by
> x(1) = 2, > y(1) = 3
> and for n >= 2 :
> x(n+1) = x(n)y(n)
> y(n+1) = x(n)y(n) + 1
> By induction, x and y stay positive. Also x(n) and y(n) are relatively
prime
> by definition. So y(n) has a prime factor which x(n) lacks, and that
factor,
> along with all the factors of x(n), appears in x(n+1). So by induction
x(n)
> has at least n distinct prime factors, for arbitrary n.
SIMPLER NN + N has more prime factors than N
"Saidak's proof" is certainly not new.
--Bill Dubuque
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