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A337783
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Even composite integers m such that U(m)^2 == 1 (mod m), where U(m)=A004187(m) is the m-th generalized Lucas number of parameters a=7 and b=1.
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1
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4, 8, 16, 44, 104, 136, 152, 164, 176, 232, 286, 442, 496, 656, 836, 856, 976, 1072, 1364, 1378, 1394, 1804, 1826, 2204, 2248, 2584, 2626, 2684, 2834, 3016, 3268, 3536, 3926, 4264, 4346, 4636, 5084, 5104, 5146, 5662, 7208, 7216, 7384, 7676, 7964, 8294, 8632, 8774, 9164, 9316, 9976
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OFFSET
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1,1
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COMMENTS
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This sequence contains the even composite integers for which the congruence holds.
The generalized Lucas sequences of integer parameters (a,b) defined by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^(p)==1 (mod p) whenever p is prime and b=-1,1.
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REFERENCES
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D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020).
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LINKS
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MATHEMATICA
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Select[Range[2, 10000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 1, #] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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