MATH 4573: Elementary Number Theory April 1
Ximera notes for April 1. We will prove quadratic reciprocity.
MATH 4573: Elementary Number Theory April 10
Ximera notes for April 10. We prove that all integers can be written as the sum of four squares.
MATH 4573: Elementary Number Theory April 13
Ximera notes for April 13. We take a number theoretic view of decimal (ie, regular) expansion of numbers.
MATH 4573: Elementary Number Theory April 15
Ximera notes for April 15. We dive into the world of continued fractions
MATH 4573: Elementary Number Theory April 17
Ximera notes for April 17. We find the continued fraction expansions of some rational and irrational numbers, and prove some theorems about errors of estimates.
MATH 4573: Elementary Number Theory April 20
Ximera notes for April 20. We explore the Farey sequence of rational numbers.
MATH 4573: Elementary Number Theory April 22
Ximera notes for April 22. We look at binary and other expansions of real numbers. We also return to Gaussian integers.
MATH 4573: Elementary Number Theory April 3
Ximera notes for April 3. Good news, everyone! We are starting Diophantine equations, which are the type of problems that Ximera can actually check. We will pause to give people a chance to solve the problem.
MATH 4573: Elementary Number Theory April 6
Ximera notes for April 6. We will prove a formula for generating Pythagorean triples. We will also prove some cases of Fermat’s Last Theorem
MATH 4573: Elementary Number Theory April 8
Ximera notes for April 8. We finally determine which integers can be written as the sum of two squares of integers!
MATH 4573: Elementary Number Theory We’re online now!
Welcome to online Elementary Number Theory! This file
MATH 4573: Elementary Number Theory March 25
Ximera notes for March 25. We will review a some points about primitive roots, quadratic residues, and the Legendre symbol from before break, then finish those sections.