Question

In: Advanced Math

Write a procedure that implements the Fermat factorization method done in Mathematica.

Expert Solution

Given a number , Fermat's factorization methods look for integers and such that . Then

and is factored.

Every positive odd integer can be represented in the form by writing (with ) and noting that this gives

Adding and subtracting

so solving for and gives

Therefore,

As the first trial for , try , where is the ceiling function. Then check if

is a square number. There are only combinations of the last two digits which a square number can assume, so most combinations can be eliminated. If is not a square number, then try

so

Continue with

so subsequent differences are obtained simply by adding two.

This is the procedure to implement Fermat factorization Method.

Colby Messinger answered 2 years ago

write a procedure that implements the Pollard rho factorization method in Mathematica.

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