Question

Consider rem( a, d ) defined as follows (for positive integers):

a.rem(a,d) = a if a < d otherwise
b.rem(a,d) = rem(a-d, d)
According to this definition, what is rem(17,4)?

Answer 1

According to the given recursive definition, rem(17, 4) is equal to 1.

Step-by-step explanation:

According to the given definition, rem(a, d) is defined as:

1. If a is less than d, then rem(a, d) is equal to a.
2. If a is greater than or equal to d, then rem(a, d) is equal to rem(a - d, d).

To find rem(17, 4), we can apply this definition:

1. 17 is greater than 4, so we apply the second part of the definition.
2. Subtracting 4 from 17, we get 13.
3. Since 13 is still greater than or equal to 4, we apply the definition again.
4. Subtracting 4 from 13, we get 9.
5. Next, we apply the definition again with 9 and 4, subtracting 4 from 9 to get 5.
6. Finally, we apply the definition a final time with 5 and 4, subtracting 4 from 5 to get 1.

Therefore, rem(17, 4) is equal to 1.