Let $p$ and $q$ be odd primes s.t. $pFermat's Factorization produce for $n = pq$? Here is some sample data I iterated: (I am having trouble solving for an explicit formula in terms of $n, p$ and $q$
FermatFactorization(15) (5)(3)
NumCycles: 1
FermatFactorization(21) (7)(3)
NumCycles: 2
FermatFactorization(33) (11)(3)
NumCycles: 5
FermatFactorization(35) (7)(5)
NumCycles: 1
FermatFactorization(39) (13)(3)
NumCycles: 6
FermatFactorization(51) (17)(3)
NumCycles: 9
FermatFactorization(55) (11)(5)
NumCycles: 3
FermatFactorization(57) (19)(3)
NumCycles: 11
FermatFactorization(65) (13)(5)
NumCycles: 4
FermatFactorization(69) (23)(3)
NumCycles: 14
FermatFactorization(77) (11)(7)
NumCycles: 2
FermatFactorization(85) (17)(5)
NumCycles: 7
FermatFactorization(87) (29)(3)
NumCycles: 19
FermatFactorization(91) (13)(7)
NumCycles: 3
FermatFactorization(93) (31)(3)
NumCycles: 21
FermatFactorization(95) (19)(5)
NumCycles: 9
- I want to find an explicit formula for the number of cycles in terms of $n, p, q$