Download Elementary Number Theory

Elementary Number Theory (All themes)
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Digits – (Natural) Numbers – Place Value-Overall terms
Digits versus Numbers
Familiarising with digits and numbers
Exposing the place values
Introducing factors, multiples, primes,perfect squares & cubes(with notation),odd and even num’
Digits in specific places
Alpharithms
Problems
Summations
Sum of the first n natural numbers
Sum of the squares of the first n natural numbers
Sum of the cubes of the first n natural numbers’
Problems
Divisibility Tests
Divisibility tests for 2,3,4,5,8,9,10,11,7,13
Co-primes product rule for divisibility
Problems
Divisibility, LCM, GCD of naturals and extended to integers
Factors, Multiples, Divisibility in natural numbers,primes,common factors and multiples, coprimes
LCM, GCD of natural numbers
Observations on divisibility
Extension of Divisibility, LCM, GCD to integers
Euclid’s lemma
Problems
Division Algorithm and it’s Applications
Division Algorithm in Z
Forms of integers and hence that of squares, cubes etc.
Application of Division Algorithm to arrive at Euclidean Algorithm to find GCD
Problems
Simple Diophantine Equations
Meaning of Diophantine Equation
Very simplest Diophantine Equation
The Simple Diophantine Equation
Problems
Theorems related to primes
Euclid’s lemma for primes
Fundamental theorem of arithmetic
Primes are infinite.
If prime p does not divide a then it divides 𝑎𝑝 - a. (Little Theorem)
Prime p divides (𝑝 − 1)! + 1. (Wilson’s theorem)
Problems
Congruences
Meaning of congruence
Properties of Congruences
Problems