Number theoryDifficulty 6.1National olympiadProve it
9. In the n-th order Farey sequence, let a/b,a′/b′ be the fractions adjacent to 1/2 on the left and right, respectively. Prove: b=b′=1+2[(n−1)/2], i.e., b is the largest odd number not exceeding n, and a+a′=b.
Solution
9. Use inductive proof.
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