Thread: GCD=1 Problem

Let r,s,t be integers. If r=st+1, prove gcd(r,s) = 1.

My works so far:

I know that to prove gcd(r,s) =1, I need to have ra + sb = 1 for some integers a and b.

Now r = st + 1 means 1 = r - st.

Well, r = r(1) and - st means + s(-b)

So 1 = r(1) + s (-t)

Is that right?

Thank you.

KK

Originally Posted by tttcomrader

Let r,s,t be integers. If r=st+1, prove gcd(r,s) = 1.

It is much simpler then that,
for .
If and only if there exists integers such as,
.

Thus, given,



Since there exists integers such that,
.
We conclude assuming that .

Haha, I was making this much harder than it has to be.

I'm glad you answered this so quickly, as this problem is due in an hour.

Thank you very much!

KK