Question
In this text, we assume that the modulus is a positive integer. But the definition of the expression a mod n also makes perfect sense if n is negative. Determine the following:
a. 7 mod 4
b. 7 mod -4
c. -7 mod 4
d. -7 mod -4
Answer
You are correct that the modulus operation can be defined for negative values of "n". In such cases, we consider the remainder to be negative or zero to maintain consistency with the definition of modulo for positive values of "n". Let's determine the results for the given expressions:
a)
Given data:7 mod 4:
When performing the modulus operation with a positive modulus, we look for the remainder when 7 is divided by 4.
7 mod 4 = 3
b)
Given data: 7 mod -4:
When performing the modulus operation with a negative modulus, we look for the remainder when 7 is divided by -4. To determine this, we consider the negative remainder values.
7 mod -4 = -1
c)
Given data:-7 mod 4:
Here, we consider the remainder when -7 is divided by 4, taking into account the negative remainder values.
-7 mod 4 = -3
d)
Given data: -7 mod -4:
Finally, let's determine the remainder when -7 is divided by -4. We consider the negative remainder values.
-7 mod -4 = -3
To summarize:
a. 7 mod 4 = 3
b. 7 mod -4 = -1
c. -7 mod 4 = -3
d. -7 mod -4 = -3