Combinatorics | Number Theory Answers

Determine the chromatic polynomial for the star S_n, where S_n is a graph with n+1 vertices consisting of n leaves all of which are adjacent to the same single vertex.

Why can't a graph with 10 vertices be isomorphic to its complement

A restaurant offers 4 different soft drink flavors, 5 different sandwiches and 3 different dessert selections. In how many ways can a person select one item from each category (a drink, a sandwich and a dessert)?

Determine if the statement is TRUE or FALSE. Justify your answer. All numbers under discussion are

integers.

7. For each m ≥ 1 and n ≥ 1, if m is even and n is odd, then m + n2 or m2 + n is prime.

8. For n ≥ 1, if n is even or divisible by 3, then n2 + n is divisible by 6.

9. For each n ≥ 1, if n is neither even nor divisible by 3, then n2 2 1 is divisible by 6

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.

If 20% of 90 mice doubled back on their tracks, 40% jumped into mouse holes, and the rest ran through water, how many ran through water?

Evaluate kronecker symbol (11/24)

In how many ways can the letters in the word MISSISSIPPI arranged?

• Show that there are infinitely many primes p≅ 1(mod5).

Determine if n=161304001 is a strong pseudo prime with respect to the base 2.