M1 Number Theory

Question 1

is about integers and their properties

Answer 1

Number theory

Question 2

basic principles of the number theory

Answer 2

divisibility

greatest common divisor

least common multiples

modular arithmetic

Question 3

divisibility test for 2

Answer 3

The last digit is even(0,2,4,6,8)

Question 4

divisibility test for 3

Answer 4

The sum of the digits is divisible by 3

Question 5

divisibility test for 4

Answer 5

The last 2 digits are divisible by 4

Question 6

divisibility test for 5

Answer 6

The last digit is 0 or 5

Question 7

divisibility test for 6

Answer 7

the number is divisible by both 2 and 3

Question 8

divisibility test for 7

Answer 8

If you double the last digit and subtract it
from the rest of the number and the answer
is 0 or
*divisible by 7

Question 9

divisibility test for 8

Answer 9

The last three digits are divisible by 8

Question 10

divisibility test for 9

Answer 10

The sum of the digits is divisible by 9
(note: you can apply this rule to that answer
again if you want)

Question 11

divisibility test for 10

Answer 11

The number ends in 0.

Question 12

divisibility test for 11

Answer 12

If you sum every second digit and then
subtract all other digits and the answer is 0 or
* divisible by 11

Question 13

divisibility test for 12

Answer 13

The number is divisible by both 3 and 43+2

Question 14

When a divides b we say that a is a X of b and

that b is a X of a.

Answer 14

factor

multiple

Question 15

The notation a | b means that a ? b.

Answer 15

divides

Question 16

We write a X b when a does not ? b.

Answer 16

divide

Question 17

if a | b and a | c, then

Answer 17

a | (b + c)

Question 18

f a | b, then

Answer 18

a | bc for all integers c

Question 19

if a | b and b | c, then

Answer 19

a | c

Question 20

A positive integer p greater than 1 is called ? if

the only positive factors of p are 1 and p.

Answer 20

prime

Question 21

A positive integer that is greater than 1 and is not

prime is called

Answer 21

composite

Question 22

The largest integer d such that d | a and d | b is called

X of a and b

Answer 22

the greatest common divisor

Question 23

Two integers a and b are X if

gcd(a, b) = 1

Answer 23

relatively prime

Question 24

The integers a1, a2, ..., an are X 
if gcd(ai, aj) = 1 whenever 1 i < j n.

Answer 24

pairwise relatively prime

Question 25

The X of the positive integers a
and b is the smallest positive integer that is divisible
by both a and b.

Answer 25

least common multiple