Lecture 15 - Factorization and Algebraic Number Theory. Lecture 16 - Pythagorean Triples.

## An Introduction to Number Theory

Lecture 17 - An Introduction to Algebraic Geometry. Lecture 19 - The Abundance of Irrational Numbers. Lecture 20 - Transcending the Algebraic Numbers. Lecture 21 - Diophantine Approximation. Lecture 23 - Applications Involving Continued Fractions.

Represent a Primitive Pythagorean Triples with a unique pair of relatively prime integers. Investigate the historical background of Fermat's Last Theorem. Primes and Greatest Common Divisions Investigate the distribution of prime numbers.

Represent integers in different bases. Find the greatest common factor using the Euclidean Algorithm. Investigate different factorization methods, such as the sieve of Eratosthenes and Fermat factorization.

Investigate the proof of the Fundamental Theorem of Arithmetic. Congruence Solve systems of linear congruences.

Solve systems of linear congruences with different moduli using the Chinese Remainder Theorem. Exercise Break the code and decipher the message.

## An Introduction to Number Theory | G. Everest | Springer

Use your program to factor the following numbers. Compute the encrypted message e 1 , e 2 he should send to Alice. Will the encrypted message be the same?