State Lagrange’s theorem about periodic continued fractions.Find the continued fraction expansion and the first 6 convergents for a = [6] Find the quadratic irrational given by the continued fraction 15;1,, 1,2, 2]. [4] (b) Find the two smallest positive solutions of Pell’s equation x2 10y2 1.

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(a) State Lagrange’s theorem about periodic continued fractions.
[3]
Find the continued fraction expansion and the first 6 convergents for a = [6] Find the quadratic irrational given by the continued fraction 15;1,, 1,2, 2]. [4] (b) Find the two smallest positive solutions of Pell’s equation x2 10y2 1.
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