172
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: + + + + + + + + + + + + + + + + + + + + +
Suggestions for a better defintion
==The square of an even number is always even, and the square of an odd number is always odd==
==The square of an even number is always even, and the square of an odd number is always odd==
Try to prove it yourself. Hint: try squaring some smallish odd and even numbers, doing the calculation in binary (base 2) arithmetic. [[User:Dpbsmith|Dpbsmith]] 20:16, 18 April 2007 (EDT)
Try to prove it yourself. Hint: try squaring some smallish odd and even numbers, doing the calculation in binary (base 2) arithmetic. [[User:Dpbsmith|Dpbsmith]] 20:16, 18 April 2007 (EDT)
==Towards a better article==
Lotsofsources to draw on, but this dicision is taken from http://www.math.uiuc.edu/ResearchAreas/numbertheory/guide.html
'''Elementary Number Theory'''
divisibility and prime factorization, residue classes, congruences, the quadratic reciprocity law, representation of numbers by forms, diophantine equations, continued fraction approximations and sieves.
'''Analytic Number Theory'''
An arithmetical phenomenon is represented by a related function, generally an analytic function of a complex variable. Information about the arithmetical problem is then extracted by analysis of the associated function.
'''Algebraic Number Theory'''
This deals with fields of algebraic numbers, that is with numbers which are roots of a polynomial equation with rational coefficients. Among areas of study are decomposition laws for primes in a number field, extensions of the famous quadratic reciprocity law and of Gauss and Jacobi sums, class numbers and units, and the connection between Stickelberger elements and p-adic L-functions.
'''Probabilistic Number Theory'''
In probabilistic number theory statistical limit theorems are established in problems involving "almost independent" random variables. Methods used include a combination of probabilistic, elementary and analytic ideas.
--[[User:AvengingAngel|AvengingAngel]] 18:36, 26 April 2007 (EDT)