List five integers that are congruent to 4 modulo 12.

Ramsey

Ramsey

Answered question

2021-09-27

List five integers that are congruent to 4 modulo 12.

Answer & Explanation

Caren

Caren

Skilled2021-09-28Added 96 answers

Definitions
a divides b if there exists an integer c such that b=ac
Notation: a|b
Division algorithm Let n be an integer and d a positive integer. Then there are unique integers q and r with 0rd such that n=dq+r
q is called the quotient and r is called the remainder
q=n÷d
r=n mod d
a is congurent to be b modulo m if m divides a-b. Notation: ab (mod m).
Solution
We need to find five integers that are in agreement with 4 modulo 12.
According to the definition of congruent modulo 12, x is congruent to 4 modulo 12, when 12 divides. x4
Since 12 divides 0,12,24,36,48,, possible values for x-4 are 0,12,28,40,52
x4=0x=4
x4=12x=16
x4=24x=28
x4=36x=40
x4=48x=52
This means that five integers that are equal to 4 when divided by 12 are 4,16,28,40, and 52.

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