Unformatted text preview: 1 . Proposition 1.6.13. Two integers m and n are relatively prime if, and only if, 1 2 I.m;n/ . Proof. Exercise 1.6.8 . n Example 1.6.14. The integers 21 and 16 are relatively prime and 1 D ² 3 ± 21 C 4 ± 16 . Proposition 1.6.15. If p is a prime number and a is any nonzero integer, then either p divides a or p and a are relatively prime. Proof. Exercise 1.6.9 . n From here, it is a only a short way to the proof of uniqueness of prime factorizations. The key observation is the following:...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Division, Remainder

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