[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= p^α₁¹ p^α₂² …p^α_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.