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Pell-type norm from a periodic continued fraction
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Area of mathematics
Number theory
Diophantine approximation
Continued fraction
Periodic continued fraction of a quadratic irrational
Continued fraction of the square root of eleven
Created
2026-09-24
Updated
2026-09-24
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For the even convergents of
11
,
p
2
m
+
q
2
m
11
=
(
3
+
11
)
(
10
+
3
11
)
m
.
(1)
Since the
second
factor has norm one, every such convergent satisfies
p
2
m
2
−
11
q
2
m
2
=
−
2
.
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Continued fraction of the square root of eleven
Periodic continued fraction of a quadratic irrational
Continued fraction
Diophantine approximation
Number theory
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2022
/
ii
/
Paper 4
/
1I
/
Solution
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