# Thread: Showing that a and b are relatively prime

1. ## Showing that a and b are relatively prime

Back again with more "optional" homework!

Question: "Let a and b be positive integers. Suppose there exist integers j and k such that aj + bk = 1. Show that a and b are relatively prime."

All I have so far is that a and b are relatively prime iff the gcd(a,b) = 1. Let a and b be elements of all positive integers.

2. ## Re: Showing that a and b are relatively prime

Use "proof by contradiction"- If a and b are not relatively prime. Then there exist positive integers, p, c, and d such that a= pc and b= pd. So aj+ bk= pcj+ pdk= p(cj+ dk)= 1.

3. ## Re: Showing that a and b are relatively prime

Thank you so much! So would that be the conclusion of the problem, or do I need a finalizing statement, something like "because the statement/work above is not true thus, a and b are relatively prime"?

4. ## Re: Showing that a and b are relatively prime

You might want to say why the statement is true!

5. ## Re: Showing that a and b are relatively prime

And that is just thing, I simply don't know WHY the statement is true!

6. ## Re: Showing that a and b are relatively prime

So would I say that because the information (that you supplied) is equal to 1, and two numbers are relatively prime if they are equal to 1?

### let a and b be positive integers. suppo

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