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Pell-type norm from a periodic continued fraction

For the even convergents of

11

,

p_{2 m} + q_{2 m} 11 = (3 + 11) (10 + 311)^{m} .

Since the second factor has norm one, every such convergent satisfies

p_{2 m}^{2} - 11 q_{2 m}^{2} = - 2

.

 Ancestors (7)

 Incoming links (1)

Solution