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Unformatted text preview: Appendix C.) 1.6.8. Show that two nonzero integers m and n are relatively prime if, and only if, 1 2 I.m;n/ . 1.6.9. Show that if p is a prime number and a is any nonzero integer, then either p divides a or p and a are relatively prime. 1.6.10. Suppose that a and b are relatively prime integers and that x is an integer. Show that if a divides the product bx , then a divides x . Hint: Use the existence of s;t such that sa C tb D 1 . 1.6.11. Suppose that a and b are relatively prime integers and that x is an integer. Show that if a divides x and b divides x , then ab divides x . 1.6.12. Show that if a prime number p divides a product a 1 a 2 :::a r of nonzero integers, then p divides one of the factors....
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- Fall '08