# Thread: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

1. ## Show there exist integers j and k such that aj + a^2b^2 + bk = 1

Question: Let a and b be relatively prime positive integers. Show there exist integers j and k such that aj + a^2b^2 + bk = 1.

I believe I have to do something like letting j and k be elements of a set of something, but I could very easily be mistaken.

2. ## Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

Hey azollner95.

The j and k are indices and the sets contain the pair of numbers where the two numbers are relatively prime.

So you have a set of pairs (ai,bj) where (ai,bj) are relatively prime.

3. ## Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

Hi chiro! When you wrote (ai,bj), did you mean 'ak', and not 'ai'?

4. ## Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

No intention to bump, but could anyone clarify on what they could have possibly meant, or if their calculations were correct/accurate.

5. ## Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

They are just indices so interpret them as that - you can make them whatever letters you like.