fermat
Mathematical Programming with Python
https://people.sc.fsu.edu/~jburkardt/classes/...
python_2025/fermat/fermat.html

fermat: with only paper and pencil available, Pierre Fermat studied prime numbers, and methods for finding factors of composite numbers. One of his methods uses an interesting algebraic approach to determine a factorization n = f1 * f2 for any integer n. For certain problems, this method is much faster than simply trying every possible divisor of n.

Lecture notes:

• fermat.pdf
• boeck.pdf, "Fermat Factorization in the Wild", discusses using Fermat factorization to break RSA encryption.
• rsa.pdf, some background on the RSA encryption method.

• fermat.py
• fermat_boeck.py, allows multiple precision arithmetic using the gmpy2 library.
• fermat_script.py, an interactive version which seeks factors of 2,027,651,281.