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Proof for: If a|bc, then a|b.

  • Thread starter DrAlexMV
  • Start date
  • #1
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In my Discrete Mathematics class we are are covering divisibility. One of the problems that the professor covered (quite terribly) is the following:

Homework Statement



Prove or salvage:

If a|bc, then a|b.

Homework Equations



Relevant concepts:

Relatively prime numbers
Divisibility

The Attempt at a Solution



I know that the statement is wrong as it is. I also know that in order to salvage the statement, I must say that a and c are relatively prime. The problem is that I do not know how to rigorously prove this.

Could somebody guide me in how to do this. Teach a man to fish!
 

Answers and Replies

  • #2
jgens
Gold Member
1,581
50
Use the following fact: If gcd(a,c)=1, then ax+cy=1 for some integers x,y.
 

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