Stuck on this CW question. have been learing about Eulcidean Algorithm and Bezouts Identity but I'm at a complete loss.

Q: Prove by induction that if r$\displaystyle _{n+1}$ is the first remainder equal to 0 in the Euclidean Algorithm then r$\displaystyle _{n+1-k}$ $\displaystyle \geq$ f$\displaystyle _{k}$

I know that proof by induction starts with a base step with n = 1; leading to the inductive step on n+1 but I'm struggling to even understand the question properly.

Any advice at all would be appreciated - I'm struggling to understand even the question. The work is due in the morning and I can't find any examples like this on the web.

Please help

Felix