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Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your previous knowledge about prime factorization or prime numbers beyond the definition (primes only have two positive divisors). Note: This is a simplified version of "If p is prime and p|(ab), then p|a or p|6." This theorem is used to prove that integers have a prime factorization, which is why we are not using prime factorization

Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your previous knowledge about prime factorization or prime numbers beyond the definition (primes only have two positive divisors). Note: This is a simplified version of "If p is prime and p|(ab), then p|a or p|6." This theorem is used to prove that integers have a prime factorization, which is why we are not using prime factorization

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...
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Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your previous knowledge about prime factorization or prime numbers beyond the definition (primes only have two positive divisors). Note: This is a simplified version of "If p is prime and p|(ab), then p|a or pl6." This theorem is used to prove that integers have a prime factorization, which is why we are not using prime factorization to prove this proposition. Hint: There are going to be several ways to prove this. One way is to find integers x and make 5x + 7y theorem mentioned in the note above. A third is by cases and using the division algorithm, but this may not be the easiest. that = 1 and use this equation in your proof. Another way is to look at a proof of the Proof.
Transcribed Image Text:Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your previous knowledge about prime factorization or prime numbers beyond the definition (primes only have two positive divisors). Note: This is a simplified version of "If p is prime and p|(ab), then p|a or pl6." This theorem is used to prove that integers have a prime factorization, which is why we are not using prime factorization to prove this proposition. Hint: There are going to be several ways to prove this. One way is to find integers x and make 5x + 7y theorem mentioned in the note above. A third is by cases and using the division algorithm, but this may not be the easiest. that = 1 and use this equation in your proof. Another way is to look at a proof of the Proof.
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