Geodesic
On reducing the order of linear recurrence equations with constant coefficients
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 12-13

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The paper deals with the relations that define non-linear recursion of the first order for a general linear recurrence relation of the second order with constant coefficients. It is proved that the linear recurrence relation of second order with constant coefficients and different roots is reduced to a non-trivial homogeneous relation of the first order iff the product of some integer degrees of these roots equals 1.
Keywords: linear recurrence relation, nonlinear recurrence relation; Fibonacci numbers, difference equations. 
@article{PDMA_2017_10_a2,
     author = {K. L. Geut and S. S. Titov},
     title = {On reducing the order of linear recurrence equations with constant coefficients},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {12--13},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a2/}
}
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K. L. Geut; S. S. Titov. On reducing the order of linear recurrence equations with constant coefficients. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 12-13. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a2/