If you have three natural numbers a, b and c.
How can you prove that for (bc), if a does not divide b and it does not divide c, then it also does not divide (bc)?
Divisor of Product
0
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elementary-number-theory
prime-numbers
divisibility
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1You can't. $4 \nmid 6$ and $4 \nmid 10$, but $4 \mid 60$. – 2017-02-01
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0ok. Now let's add that all three numbers are prime numbers. Would the statement then be true and if yes why? – 2017-02-01
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1It suffices to require that $a$ is prime. Depending on context, that can be essentially the definition of prime, or Euclid's lemma. – 2017-02-01
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0What if b and c are prime, how can you prove that a, also prime, does not divide the product of b and c? – 2017-02-01
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0What is the definition of a prime you're using? – 2017-02-01
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02,3 ,5 , 7 ,... – 2017-02-01