M1 Number Theory Flashcards
is about integers and their properties
Number theory
basic principles of the number theory
divisibility
greatest common divisor
least common multiples
modular arithmetic
divisibility test for 2
The last digit is even(0,2,4,6,8)
divisibility test for 3
The sum of the digits is divisible by 3
divisibility test for 4
The last 2 digits are divisible by 4
divisibility test for 5
The last digit is 0 or 5
divisibility test for 6
the number is divisible by both 2 and 3
divisibility test for 7
If you double the last digit and subtract it
from the rest of the number and the answer
is 0 or
*divisible by 7
divisibility test for 8
The last three digits are divisible by 8
divisibility test for 9
The sum of the digits is divisible by 9
(note: you can apply this rule to that answer
again if you want)
divisibility test for 10
The number ends in 0.
divisibility test for 11
If you sum every second digit and then
subtract all other digits and the answer is 0 or
* divisible by 11
divisibility test for 12
The number is divisible by both 3 and 43+2
When a divides b we say that a is a X of b and
that b is a X of a.
factor
multiple
The notation a | b means that a ? b.
divides
We write a X b when a does not ? b.
divide
if a | b and a | c, then
a | (b + c)
f a | b, then
a | bc for all integers c
if a | b and b | c, then
a | c
A positive integer p greater than 1 is called ? if
the only positive factors of p are 1 and p.
prime
A positive integer that is greater than 1 and is not
prime is called
composite
The largest integer d such that d | a and d | b is called
X of a and b
the greatest common divisor
Two integers a and b are X if
gcd(a, b) = 1
relatively prime
The integers a1, a2, ..., an are X if gcd(ai, aj) = 1 whenever 1 i < j n.
pairwise relatively prime
The X of the positive integers a
and b is the smallest positive integer that is divisible
by both a and b.
least common multiple
