Basic Examples (2) 

A trivial factorization for Fermat's algorithm:

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A slightly larger example:

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Scope (2) 

In the following example, we see that the factor returned by FactorIntegerFermat is close to :

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The ratio of size difference between the square root and a factor to the size of the square root is around 1/2, which means the factor is removed from the square root of bign by approximately its fourth root.

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FactorIntegerFermat scales well to larger semiprimes, providing the two primes are close to :

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Options (2) 

MaxIterations (2) 

Factoring the following semiprime requires 262143 iterations, which is more than the default number of iterations (2¹⁶):

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Increasing MaxIterations obtains the factorization:

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Properties and Relations (2) 

Lehman extended Fermat's algorithm to factor N=p q using a rational approximation to the ratio of the factors, p/q:

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This works as 10277/1199 is a good approximation to p/q:

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Possible Issues (3) 

Unlike FactorInteger, FactorIntegerFermat is not a general purpose factoring algorithm:

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FactorInteger succeeds:

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FactorIntegerFermat does not handle this case:

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