This page is dedicated to Shaheed Bhai Mohar Singh Ji.
Photo of classroom activity:
Largest known prime at present is the Mersenne prime
Mp = 2 77 232 917 – 1
This number was found in December 2017 and it has 23,249,425 digits.
The largest known perfect number PN is
PN = (2 77 232 917 – 1)X Mp
Hardy (1877 – 1947) and Ramanujan (1887 – 1920).
The mathematicians patterns, like a painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
G.H. Hardy in A Mathematicians Apology
William Thurston 1946 to 2012
I think most mathematicians love mathematics for mathematics’ sake. They really do like the feeling of being in an ivory tower. For the most part, they are motivated by applications. But I believe that, whatever their personal motivation is doing for mathematics, in most cases the mathematics they generate will ultimately have significant applications. The important thing is to do mathematics. But, of course, it’s important to have people thinking about applications too.
Notes on Number Theory
Corrections by Dr. Giovanna Scataglini Belghitar
Investigation in Cryptography by Shannon O’Brien is here.
|Introductory chapter notes and exercises||Complete solutions to Introductory chapter|
|Summary of results of Introductory Chapter||Appendix A|
Alan Turing 1912-1954
If you are an academic and would like complete solutions to the supplementary problems then send me an email by using your university email:
Chapter 1: Introduction to Number Theory
Chapter 2: Primes and Their Distribution
Chapter 3: Modular Arithmetic
Chapter 4: A Survey of Linear Congruences
Chapter 5: Eulerâ€™s Generalization of Fermatâ€™s Theorem
Euler 1707 to 1783
Chapter 6: Primitive Roots and Indices
Chapter 7: Quadratic Residues
Chapter 15: Continued Fractions
|Section 15.1||Exercise 15.1||Complete solutions to Exercise 15.1|
|Section 15.2||Exercise 15.2||Complete solutions to Exercise 15.2|
|Section 15.3 Applying convergents||Exercise 15.3||Complete solutions to Exercise 15.3|