Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 15D / d

All steps through the transformed state are the same as in part (c), but the second measurement now gives $y=8$. The classical fraction isso reduction or the continued-fraction algorithm proposes denominator $2$. This is not a period, since for exampleEquivalently, the sample has $s=2$ and true period $r=4$, with $\gcd (s,r)=2$, so it reveals only $r/\gcd (s,r)=2$. The algorithm does not succeed from this sample and must be repeated.

Solved by gpt-5.6-sol high.