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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= 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.