2. (Number Theory - 20 pt.) a. (5 pts.) Show that if a, b, c, and m are integers with m 2 2,c> O and a = b (mod m) then ac = bc (mod mc) b. (15 pt.) A hashing function h assigns memory location h(k) to the record that has k as its key. One of the most common is the function h(k) = k mod m where m is the number of available memory locations. Because a hashing function is not one-to-one, more than one record may be assigned to a memory location. When this happens, we say that a collision occurs. For collision, we can use a linear probing function, namely h{k, i) = (h(k) +i) mod m, where i is the number of collisions occurred for the current key. Consider h (k) = k mod 7 as the hash function and place the following values in the hash table: 2, 4, 12, 19 0 1 2 3 4 5 6