[Solved] MME529 Homework #2

Page 37 Burton please do problems 1,2,3,5,6

additionally:

1. Suppose x is an integer and someone has applied the Fundamental Theorem of Arithmetic to it, obtaining x= p₁¹ p₂² p_nⁿ What would x³ look like? What generalization can you make out of this?

2. If p is a prime number, does px ky = 1 have solutions ? k could be any integer here.

3. If p is a prime number, argue why p must divide C_p,r (binomial coefficient)

4. See if you can prove the following:

if x divides the product bc and x is prime then x divides either b or c.

Make up a counterexample where x is not prime and x divides their product but not either one.