We introduce Fermat’s Christmas Theorem and try to understand its meaning through concrete examples.
Expository tour of Euclid’s proof that there are infinitely many primes, preceded by a discussion of Euclidean division and the fundamental theorem of arithmetic.
We introduce modular arithmetic and understand the meaning of Chinese Remainder Theorem.
We prove Fermat’s Christmas Theorem using Gaussian integers, linking sums of two squares to the solvability of \(x^2\equiv_p -1\).