2.3 Integers Modulo Flashcards
1
Q
what does a ≡ b mean
A
if m >= 2 is an integer, we say that the integers a and b are equivalent modulo m if they leave the same remainder when divided by m
We write a ≡ b mod m
2
Q
is 13 ≡ 6 mod 7 correct
A
yes
3
Q
is 13 ≡ 2 mod 7 correct
A
no
4
Q
is 15 ≡ 0 mod 5 correct
A
yes
5
Q
if a1 ≡ a2 mod m and b1 ≡ b2 mod m, write the two new formulas
A
(a1 + b1) ≡ (a2 + b2) mod m
(a1 * b1) ≡ (a2 * b2)
6
Q
What does ax ≡ b mod m mean
A
when you divide ax by m you get a remainder of b
7
Q
rewrite ax ≡ b mod m in terns od b
A
b = ax + my
(y is just some multiple of m)
8
Q
rewrite 35x ≡ 21 mod 91 as a linear diophantine equation
A
35x + 91y = 21
9
Q
Solve 35x = 21 mod 91
A
x ≡ -15 mod 13
10
Q
A
