User:Marty/UCSC Math 110 Fall 2008/Week 2

This week, we are covering applications of the "canonical decomposition", including the following:
 * Connections between divisibility and the canonical decomposition.
 * Relations among the GCD and LCM. (Covers::State/Minmax addition formula, Covers::State/Canonical decompositions can be used to find GCD and LCM)
 * Completing the study of linear Diophantine equations. ( Covers::State/Solutions to homogeneous linear Diophantine equations can be found with the LCM )
 * Counting multiples and the floor function. Covers::State/Counting multiples of d between 1 and n, Covers::Def/Floor, Covers::State/The floor sum identity.
 * Chebyshev's approach to the prime number theorem. (Covers::State/Canonical decompositions of factorials, Covers::State/Canonical decompositions of binomial coefficients,, Covers::State/Chebyshev estimates for the prime number function)