Divisibility and Modular Arithmetic

Learning tasks

A) Divisibility
1) Analyzing Divisibility Properties	Ex 1 Ex 2 Ex 3 Ex 4 Ex 5 Ex 6
2) Writing Direct Proofs in Arithmetic	Ex 7 Ex 8 Ex 9 Ex 10 Ex 11 Ex 12 Ex 13 Ex 14
3) Constructing Proofs by Exhaustion	Ex 15 Ex 16
4) Constructing Proofs by Contrapositive	Ex 17 Ex 18
5) Constructing Proofs of Equivalence	Ex 19 Ex 20
6) Solving Diophantine Equations	Ex 21 Ex 22 Ex 23 Ex 24
B) Euclidean Division (Division with Remainder)
7) Practicing Divisibility Proofs	Ex 25 Ex 26 Ex 27 Ex 28 Ex 29
8) Calculating the Division with Remainders	Ex 30 Ex 31 Ex 32 Ex 33 Ex 34
9) Applying and Manipulating Euclidean Division	Ex 35 Ex 36 Ex 37 Ex 38 Ex 39
C) Congruences
10) Analyzing Congruence Properties	Ex 40 Ex 41 Ex 42 Ex 43 Ex 44 Ex 45
11) Determining Remainders of Large Powers	Ex 46 Ex 47 Ex 48 Ex 49
12) Proving and Applying Divisibility Criteria	Ex 50 Ex 51 Ex 52
13) Manipulating and Solving Congruence Equations	Ex 53 Ex 54 Ex 55

Lesson
Text book

Exercises Correction
A) Divisibility
    1) Analyzing Divisibility Properties Ex 1 Ex 2 Ex 3 Ex 4 Ex 5 Ex 6
    2) Writing Direct Proofs in Arithmetic Ex 7 Ex 8 Ex 9 Ex 10 Ex 11 Ex 12 Ex 13 Ex 14
    3) Constructing Proofs by Exhaustion Ex 15 Ex 16
    4) Constructing Proofs by Contrapositive Ex 17 Ex 18
    5) Constructing Proofs of Equivalence Ex 19 Ex 20
    6) Solving Diophantine Equations Ex 21 Ex 22 Ex 23 Ex 24
B) Euclidean Division (Division with Remainder)
    7) Practicing Divisibility Proofs Ex 25 Ex 26 Ex 27 Ex 28 Ex 29
    8) Calculating the Division with Remainders Ex 30 Ex 31 Ex 32 Ex 33 Ex 34
    9) Applying and Manipulating Euclidean Division Ex 35 Ex 36 Ex 37 Ex 38 Ex 39
C) Congruences
    10) Analyzing Congruence Properties Ex 40 Ex 41 Ex 42 Ex 43 Ex 44 Ex 45
    11) Determining Remainders of Large Powers Ex 46 Ex 47 Ex 48 Ex 49
    12) Proving and Applying Divisibility Criteria Ex 50 Ex 51 Ex 52
    13) Manipulating and Solving Congruence Equations Ex 53 Ex 54 Ex 55