Junior_8.5

Date	Activities / Objectives	Images / Home work / Assignments	Remarks / Images	References / Links
Monday April 11 16:00 -17:30	Registration Forms Introduction to activities FORMAL ARITHMETIC Definition of GCD(a;b) Definition of LCM(a;b) AMC sample problems	AMC 10 Sample problems #1	Course will be divided into two main activities : Formal Arithmetic AMC 10 training A merican M athematics C ompetition	AMC 10 Sample problems #1 Memo /Arithmetic DEFINITIONS
Monday April 18 16:00 -17:30	FORMAL ARITHMETIC Demonstration of the main Theorems Euclidian division : a = b.q + r , 0 ≤ r < b GCD(a;b) = GCD(b;r) GCD construction Bézout theorem : GCD(a;b)=1 <=> a.u + b.v = 1 GCD(a;b)=d <=> a.u + b.v = d GAUSS THEOREM : GCD(a;b)=1 & a \| bc => a \| c	Arithmetic Theorems to be proved Exercises to prepare AMC 10 Sample problems #2		Arithmetic Theorems to be proved Exercises to prepare AMC 10 Sample problems #2
Monday April 25 16:00 -17:00	FORMAL ARITHMETIC : Review of the 10 main Theorems Demo of # 8 - 9 - 10 TYPICAL EXERCISE : applications of Bézout & Gauss : DIOPHANTINE EQUATION : 8 x + 5 y = 1	Arithmetic Theorems to be proved Exercises to prepare AMC 10 Sample problems #2		Arithmetic Theorems to be proved AMC 10 Sample problems