1. Suppose x is an integer and someone has applied the Fundamental Theorem of Arithmetic to it, obtaining x= pα11 pα22 ...pαnn 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 Cp,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.
