Let $p$ and $q$ be odd primes s.t. $p and $n= pq$. How many cycles will Fermat'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 $n, p, q$