Pell Numbers, Pell–Lucas Numbers and Modular Group
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We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m ≥ 1) of the modular group PSL(2,Z) = 〈x,y : x2 = y3 = 1〉, where [Formula: see text] and [Formula: see text], is a 2 × 2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell–Lucas number. If g fixes elements of [Formula: see text], where d is a square-free positive number, on the circuit of the coset diagram, then d = 2 and there are only four pairs of ambiguous numbers on the circuit.
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1983 ◽
Vol 66
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pp. 331-341
1990 ◽
Vol 32
(3)
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pp. 317-327
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1974 ◽
Vol 10
(2)
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pp. 245-253
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1991 ◽
Vol 14
(4)
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pp. 697-703
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1990 ◽
Vol 33
(1)
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pp. 1-10
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2006 ◽
Vol 90
(518)
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pp. 215-222
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