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and 
intersect at two points 
and 
. Let 
be the line tangent to these circles at 
and 
, respectively, so that lies closer to than . Let 
be the line parallel to and passing through the point , with 
on and 
on . Lines 
and 
meet at 
; lines 
and meet at 
; lines 
and meet at 
. Show that 
.
is such that 
for any positive integers 
. Assume there exists a positive integer 
such that 
for all positive integers 
. Determine all possible values of 
.
satisfy that 
. Prove that: 
be a prime number, and 
be a sequence defined by 
and 
, 
. Show that one of the first 
terms of the sequence is not prime.
Then, by Fermat 