Editing Carmichael's theorem (section)

==Fibonacci and Pell cases==
The only exceptions in Fibonacci case for ''n'' up to 12 are:

:F(1)&nbsp;=&nbsp;1 and F(2)&nbsp;=&nbsp;1, which have no prime divisors
:F(6)&nbsp;=&nbsp;8, whose only prime divisor is 2 (which is F(3))
:F(12)&nbsp;=&nbsp;144, whose only prime divisors are 2 (which is F(3)) and 3 (which is F(4))

The smallest primitive prime divisor of F(''n'') are
:1, 1, 2, 3, 5, 1, 13, 7, 17, 11, 89, 1, 233, 29, 61, 47, 1597, 19, 37, 41, 421, 199, 28657, 23, 3001, 521, 53, 281, 514229, 31, 557, 2207, 19801, 3571, 141961, 107, 73, 9349, 135721, 2161, 2789, 211, 433494437, 43, 109441, ... {{OEIS|id=A001578}}
Carmichael's [[theorem]] says that every Fibonacci number, apart from the exceptions listed above, has at least one primitive prime divisor.

If ''n''&nbsp;>&thinsp;1, then the ''n''th [[Pell number]] has at least one prime divisor that does not divide any earlier Pell number. The smallest primitive prime divisor of ''n''th Pell number are
:1, 2, 5, 3, 29, 7, 13, 17, 197, 41, 5741, 11, 33461, 239, 269, 577, 137, 199, 37, 19, 45697, 23, 229, 1153, 1549, 79, 53, 113, 44560482149, 31, 61, 665857, 52734529, 103, 1800193921, 73, 593, 9369319, 389, 241, ... {{OEIS|id=A246556}}