Question: . The Euclidean state machine is defined by the rule . x; y / ! . y; rem.x; y / / ; ( 9 .

.
The Euclidean state machine is defined by the rule
.x; y/!.y; rem.x; y//; (9.18)
for y >0.
Prove that the smallest positive integers a b for which, starting in state .a; b/,
the state machine will make n transitions are F .n C 1/ and F .n/, where F .n/ is
the nth Fibonacci nu

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