Question

An integer m divides n, denoted as m | n, if there exists an integer k such that:

a) n = mk
b) n = m + k
c) n = mk + 1
d) n = m/k

Answer 1

An integer m divides n if there exists an integer k such that: n = mk, n = m + k, n = mk + 1, or n = m/k.

Step-by-step explanation:

An integer m divides n if there exists an integer k such that:

1. n = mk
2. n = m + k
3. n = mk + 1
4. n = m/k

To determine the allowed values of m and k for a given value of n, we must examine each condition. For example, for condition a) n = mk, if n = 12, then m can be 1, 2, 3, 4, 6, or 12, and k can be 12, 6, 4, 3, 2, or 1, respectively.

Similarly, for condition b) n = m + k, if n = 12, then m can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, and k can be 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, or 0, respectively.