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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 n x p p pn
α α α … 1 2 = 1 2 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.